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Derivada de:
Derivada de (60-x)*e^(x+60)
Derivada de 5*x/(x+1)
Derivada de 5x^8-8x+1
Derivada de (5x)
Expresiones idénticas
((xln^ tres (x)sqrt(x^ cinco + nueve))/(ctgx(2x^ cuatro + cinco)^ cinco))^(uno / ocho)
((xln al cubo (x) raíz cuadrada de (x en el grado 5 más 9)) dividir por (ctgx(2x en el grado 4 más 5) en el grado 5)) en el grado (1 dividir por 8)
((xln en el grado tres (x) raíz cuadrada de (x en el grado cinco más nueve)) dividir por (ctgx(2x en el grado cuatro más cinco) en el grado cinco)) en el grado (uno dividir por ocho)
((xln^3(x)√(x^5+9))/(ctgx(2x^4+5)^5))^(1/8)
((xln3(x)sqrt(x5+9))/(ctgx(2x4+5)5))(1/8)
xln3xsqrtx5+9/ctgx2x4+551/8
((xln³(x)sqrt(x⁵+9))/(ctgx(2x⁴+5)⁵))^(1/8)
((xln en el grado 3(x)sqrt(x en el grado 5+9))/(ctgx(2x en el grado 4+5) en el grado 5)) en el grado (1/8)
xln^3xsqrtx^5+9/ctgx2x^4+5^5^1/8
((xln^3(x)sqrt(x^5+9)) dividir por (ctgx(2x^4+5)^5))^(1 dividir por 8)
Expresiones semejantes
((xln^3(x)sqrt(x^5+9))/(ctgx(2x^4-5)^5))^(1/8)
((xln^3(x)sqrt(x^5-9))/(ctgx(2x^4+5)^5))^(1/8)

Derivada de la función/ ((xln^3(x)sqrt(x^5+9))/(ctgx(2x^4+5)^5))^(1/8)

Derivada de ((xln^3(x)sqrt(x^5+9))/(ctgx(2x^4+5)^5))^(1/8)

Solución

Ha introducido [src]

        _______________________
       /              ________ 
      /       3      /  5      
     /   x*log (x)*\/  x  + 9  
    /    --------------------- 
   /                        5  
8 /               /   4    \   
\/         cot(x)*\2*x  + 5/

$$\sqrt[8]{\frac{x \log{\left(x \right)}^{3} \sqrt{x^{5} + 9}}{\left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}}}$$

(((x*log(x)^3)*sqrt(x^5 + 9))/((cot(x)*(2*x^4 + 5)^5)))^(1/8)

Solución detallada

Sustituimos $u = \frac{x \log{\left(x \right)}^{3} \sqrt{x^{5} + 9}}{\left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}}$ .
Según el principio, aplicamos: $\sqrt[8]{u}$ tenemos $\frac{1}{8 u^{\frac{7}{8}}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \frac{x \log{\left(x \right)}^{3} \sqrt{x^{5} + 9}}{\left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}}$ :
1. Se aplica la regla de la derivada parcial:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}$ y $g{\left(x \right)} = \left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}$ .
  
  Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} h{\left(x \right)} = f{\left(x \right)} g{\left(x \right)} \frac{d}{d x} h{\left(x \right)} + f{\left(x \right)} h{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} h{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Según el principio, aplicamos: $x$ tenemos $1$
    $g{\left(x \right)} = \sqrt{x^{5} + 9}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. Sustituimos $u = x^{5} + 9$ .
    2. Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(x^{5} + 9\right)$ :
      1. diferenciamos $x^{5} + 9$ miembro por miembro:
        
        La derivada de una constante $9$ es igual a cero.
        
        Según el principio, aplicamos: $x^{5}$ tenemos $5 x^{4}$
        
        Como resultado de: $5 x^{4}$
      Como resultado de la secuencia de reglas:
      
      $\frac{5 x^{4}}{2 \sqrt{x^{5} + 9}}$
    $h{\left(x \right)} = \log{\left(x \right)}^{3}$ ; calculamos $\frac{d}{d x} h{\left(x \right)}$ :
    1. Sustituimos $u = \log{\left(x \right)}$ .
    2. Según el principio, aplicamos: $u^{3}$ tenemos $3 u^{2}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \log{\left(x \right)}$ :
      1. Derivado $\log{\left(x \right)}$ es $\frac{1}{x}$ .
      Como resultado de la secuencia de reglas:
      
      $\frac{3 \log{\left(x \right)}^{2}}{x}$
    Como resultado de: $\frac{5 x^{5} \log{\left(x \right)}^{3}}{2 \sqrt{x^{5} + 9}} + \sqrt{x^{5} + 9} \log{\left(x \right)}^{3} + 3 \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}$
  Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
  1. Se aplica la regla de la derivada de una multiplicación:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = \left(2 x^{4} + 5\right)^{5}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
    1. Sustituimos $u = 2 x^{4} + 5$ .
    2. Según el principio, aplicamos: $u^{5}$ tenemos $5 u^{4}$
    3. Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \left(2 x^{4} + 5\right)$ :
      1. diferenciamos $2 x^{4} + 5$ miembro por miembro:
        
        La derivada de una constante $5$ es igual a cero.
        
        La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
        
        Según el principio, aplicamos: $x^{4}$ tenemos $4 x^{3}$
        
        Entonces, como resultado: $8 x^{3}$
        
        Como resultado de: $8 x^{3}$
      Como resultado de la secuencia de reglas:
      
      $40 x^{3} \left(2 x^{4} + 5\right)^{4}$
    $g{\left(x \right)} = \cot{\left(x \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
    1. Hay varias formas de calcular esta derivada.
      Method #1
      
      Reescribimos las funciones para diferenciar:
      
      $\cot{\left(x \right)} = \frac{1}{\tan{\left(x \right)}}$
      
      Sustituimos $u = \tan{\left(x \right)}$ .
      
      Según el principio, aplicamos: $\frac{1}{u}$ tenemos $- \frac{1}{u^{2}}$
      
      Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} \tan{\left(x \right)}$ :
      
      Reescribimos las funciones para diferenciar:
      
      $\tan{\left(x \right)} = \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
      
      Se aplica la regla de la derivada parcial:
      
      $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
      
      $f{\left(x \right)} = \sin{\left(x \right)}$ y $g{\left(x \right)} = \cos{\left(x \right)}$ .
      
      Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
      
      La derivada del seno es igual al coseno:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
      
      Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
      
      La derivada del coseno es igual a menos el seno:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
      
      Ahora aplicamos la regla de la derivada de una divesión:
      
      $\frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
      
      Como resultado de la secuencia de reglas:
      
      $- \frac{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}$
      Method #2
      
      Reescribimos las funciones para diferenciar:
      
      $\cot{\left(x \right)} = \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
      
      Se aplica la regla de la derivada parcial:
      
      $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
      
      $f{\left(x \right)} = \cos{\left(x \right)}$ y $g{\left(x \right)} = \sin{\left(x \right)}$ .
      
      Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
      
      La derivada del coseno es igual a menos el seno:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
      
      Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
      
      La derivada del seno es igual al coseno:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
      
      Ahora aplicamos la regla de la derivada de una divesión:
      
      $\frac{- \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}$
    Como resultado de: $40 x^{3} \left(2 x^{4} + 5\right)^{4} \cot{\left(x \right)} - \frac{\left(2 x^{4} + 5\right)^{5} \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}$
  Ahora aplicamos la regla de la derivada de una divesión:
  
  $\frac{- x \sqrt{x^{5} + 9} \left(40 x^{3} \left(2 x^{4} + 5\right)^{4} \cot{\left(x \right)} - \frac{\left(2 x^{4} + 5\right)^{5} \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}\right) \log{\left(x \right)}^{3} + \left(2 x^{4} + 5\right)^{5} \left(\frac{5 x^{5} \log{\left(x \right)}^{3}}{2 \sqrt{x^{5} + 9}} + \sqrt{x^{5} + 9} \log{\left(x \right)}^{3} + 3 \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}\right) \cot{\left(x \right)}}{\left(2 x^{4} + 5\right)^{10} \cot^{2}{\left(x \right)}}$
Como resultado de la secuencia de reglas:

$\frac{\frac{\left(2 x^{4} + 5\right)^{\frac{35}{8}}}{\left(\frac{x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}}{\cot{\left(x \right)}}\right)^{\frac{7}{8}}} \left(- x \sqrt{x^{5} + 9} \left(40 x^{3} \left(2 x^{4} + 5\right)^{4} \cot{\left(x \right)} - \frac{\left(2 x^{4} + 5\right)^{5} \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{\cos^{2}{\left(x \right)} \tan^{2}{\left(x \right)}}\right) \log{\left(x \right)}^{3} + \left(2 x^{4} + 5\right)^{5} \left(\frac{5 x^{5} \log{\left(x \right)}^{3}}{2 \sqrt{x^{5} + 9}} + \sqrt{x^{5} + 9} \log{\left(x \right)}^{3} + 3 \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}\right) \cot{\left(x \right)}\right)}{8 \left(2 x^{4} + 5\right)^{10} \cot^{2}{\left(x \right)}}$
Simplificamos:

$\frac{\left(- \frac{x \left(x^{5} + 9\right) \left(- 2 x^{4} + 20 x^{3} \sin{\left(2 x \right)} - 5\right) \log{\left(x \right)}}{8} + \frac{\left(2 x^{4} + 5\right) \left(5 x^{5} \log{\left(x \right)} + 2 \left(x^{5} + 9\right) \left(\log{\left(x \right)} + 3\right)\right) \sin{\left(2 x \right)}}{32}\right) \log{\left(x \right)}^{2}}{\left(x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3} \tan{\left(x \right)}\right)^{\frac{7}{8}} \left(2 x^{4} + 5\right)^{\frac{13}{8}} \sqrt{x^{5} + 9} \cos^{2}{\left(x \right)}}$

Respuesta:

$\frac{\left(- \frac{x \left(x^{5} + 9\right) \left(- 2 x^{4} + 20 x^{3} \sin{\left(2 x \right)} - 5\right) \log{\left(x \right)}}{8} + \frac{\left(2 x^{4} + 5\right) \left(5 x^{5} \log{\left(x \right)} + 2 \left(x^{5} + 9\right) \left(\log{\left(x \right)} + 3\right)\right) \sin{\left(2 x \right)}}{32}\right) \log{\left(x \right)}^{2}}{\left(x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3} \tan{\left(x \right)}\right)^{\frac{7}{8}} \left(2 x^{4} + 5\right)^{\frac{13}{8}} \sqrt{x^{5} + 9} \cos^{2}{\left(x \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                                              /                   /   ________                             5    3   \                                                                                  \       
                                                              |        1          |  /  5      /   3           2   \    5*x *log (x)|                                                                                  |       
                                                              |------------------*|\/  x  + 9 *\log (x) + 3*log (x)/ + -------------|                                                                                  |       
       __________________________________________             |          5        |                                         ________|        ________         /            5                                  4       \|       
      /      ________                                       5 |/   4    \         |                                        /  5     |       /  5         3    |  /   4    \  /        2   \       3 /   4    \        ||       
     /      /  5         3            1           /   4    \  |\2*x  + 5/ *cot(x) \                                    2*\/  x  + 9 /   x*\/  x  + 9 *log (x)*\- \2*x  + 5/ *\-1 - cot (x)/ - 40*x *\2*x  + 5/ *cot(x)/|       
    /   x*\/  x  + 9 *log (x)*------------------ *\2*x  + 5/ *|---------------------------------------------------------------------- + -------------------------------------------------------------------------------|*cot(x)
   /                                    5                     |                                  8                                                                               10                                    |       
8 /                           /   4    \                      |                                                                                                        /   4    \      2                               |       
\/                            \2*x  + 5/ *cot(x)              \                                                                                                      8*\2*x  + 5/  *cot (x)                            /       
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                          ________                                                                                                             
                                                                                                         /  5         3                                                                                                        
                                                                                                     x*\/  x  + 9 *log (x)

$$\frac{\sqrt[8]{x \frac{1}{\left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}} \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}} \left(2 x^{4} + 5\right)^{5} \left(\frac{x \sqrt{x^{5} + 9} \left(- 40 x^{3} \left(2 x^{4} + 5\right)^{4} \cot{\left(x \right)} - \left(2 x^{4} + 5\right)^{5} \left(- \cot^{2}{\left(x \right)} - 1\right)\right) \log{\left(x \right)}^{3}}{8 \left(2 x^{4} + 5\right)^{10} \cot^{2}{\left(x \right)}} + \frac{\frac{1}{\left(2 x^{4} + 5\right)^{5} \cot{\left(x \right)}} \left(\frac{5 x^{5} \log{\left(x \right)}^{3}}{2 \sqrt{x^{5} + 9}} + \sqrt{x^{5} + 9} \left(\log{\left(x \right)}^{3} + 3 \log{\left(x \right)}^{2}\right)\right)}{8}\right) \cot{\left(x \right)}}{x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}}$$

Simplificar

Segunda derivada [src]

                              /   /                                                    ________                                                   \         /                                                    ________                                                   \          /                                                    ________                                                   \     /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \      /                                                    ________                                                   \   /                                                    ________                                                   \                                                                                                                             /                                                    ________                                                   \\
                              |   |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |         |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |          |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |     |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |   |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \                    |       ________                   5                /      5  /  /       2   \ /       4\       3       \       ||
                              |   |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|       3 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|        2 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|     |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|      |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|   |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       |      /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)||
      _______________________ |16*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   40*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   640*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   8*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   48*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   |- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|   16*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------||
     /      ________          |   |                                  ________                           /       4\                                |         |                                  ________                           /       4\                                |          |                                  ________                           /       4\                                |     |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |      |                                  ________                           /       4\                                |   |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       |                    |                                  ________                           /       4\                                ||
    /      /      5     3     |   |                                 /      5                            \5 + 2*x /*cot(x)                         |         |                                 /      5                            \5 + 2*x /*cot(x)                         |          |                                 /      5                            \5 + 2*x /*cot(x)                         |     |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |      |                                 /      5                            \5 + 2*x /*cot(x)                         |   |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       |                    |                                 /      5                            \5 + 2*x /*cot(x)                         ||
   /   x*\/  9 + x  *log (x)  |   \                               \/  9 + x                                                                       /         \                               \/  9 + x                                                                       /          \                               \/  9 + x                                                                       /     \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /      \                               \/  9 + x                                                                       /   \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /                    \                               \/  9 + x                                                                       /|
8 /    --------------------- *|-------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------|
\/             cot(x)         |                                                         ________                                                                                                                    3/2                                                                                                                        ________                                                                                                                                                                                                                                                                                                                                                                                                  ________                                                                                                                                                                                                                                                                                                                                                                                                        ________                                                                                                                                                               2 /     5\                                                                                                                                                                          ________                                                              |
                              |                                                    2   /      5                                                                                                             /     5\                                                                                                             /       4\   /      5                                                                                                                                                                                                                                                                                                                                                                                                  /      5                                                                                                                                                                                                                                                                                                                                                                                                    2   /      5                                                                                                                                                               x *\9 + x /*log(x)                                                                                                                                                                  /      5                                                               |
                              \                                                   x *\/  9 + x                                                                                                              \9 + x /                                                                                                             \5 + 2*x /*\/  9 + x                                                                                                                                                                                                                                                                                                                                                                                               x*\/  9 + x  *log(x)                                                                                                                                                                                                                                                                                                                                                                                           x *\/  9 + x  *log(x)                                                                                                                                                                                                                                                                                                                                       x*\/  9 + x  *cot(x)                                                       /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5/8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /       4\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          256*\5 + 2*x /   *log(x)

$$\frac{\sqrt[8]{\frac{x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}}{\cot{\left(x \right)}}} \left(\frac{40 x^{3} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(x^{5} + 9\right)^{\frac{3}{2}}} - \frac{640 x^{2} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9}} + \frac{16 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{8 \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x \sqrt{x^{5} + 9} \log{\left(x \right)}} - \frac{\left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)}} + \frac{16 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{2} \sqrt{x^{5} + 9}} + \frac{48 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{2} \sqrt{x^{5} + 9} \log{\left(x \right)}}\right)}{256 \left(2 x^{4} + 5\right)^{\frac{5}{8}} \log{\left(x \right)}}$$

Simplificar

Tercera derivada [src]

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             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                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |      9    2           /      5                     4              4    2          4                    |                                             |      9    2           /      5                     4              4    2          4                    |                                                                                                      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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  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                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /       2   \ |  25*x *log (x)   12*\/  9 + x  *(2 + log(x))   30*x *log(x)   50*x *log (x)   10*x *(3 + log(x))*log(x)|                                           3 |  25*x *log (x)   12*\/  9 + x  *(2 + log(x))   30*x *log(x)   50*x *log (x)   10*x *(3 + log(x))*log(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /                                                                                                                                                                                                                                                                                                                                                                                                  /         2           3  \                                                                                                                \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            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                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        2*\1 + cot (x)/*|- ------------- + --------------------------- + ------------ + ------------- + -------------------------|*log(x)                                80*x *|- ------------- + --------------------------- + ------------ + ------------- + -------------------------|*log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             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                                                                                                                                                                 5    2    |  1 + cot (x)    40*x   |                                                                                                                |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            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                              |          /                                                    ________                                                   \       /                                                    ________                                                   \           /                                                    ________                                                   \             /                                                    ________                                                   \           /                                                    ________                                                   \           /                                                    ________                                                   \        /                                                    ________                                                   \        /                                                    ________                                                   \                     /                                                    ________                                                   \      |                                                                                                   /                        ________                                                                        \                                                               /                           2                                               \         ________                                                                                                                              |           3/2                 x                   ________        ________              ________       |                                             |           3/2                 x                   ________        ________              ________       |                ________         /                          2                                                                                \         ________         /                          2                                                                                \              ________                                                                  ________                                                                                                                                ________         /                          2                                                                                \                                                                       ________         /               2           3                                                                         2                             3                                         2                                                       2                     \         ________                                                             ________                                                                           ________                                                                    /                          2                                                                                \         ________                                                                                                                                                                                                           ________                                                                  ________                                                                             ________                                                                                       2    ________                                                               ________                       /                          2                                                                                \                                                                          |       /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \          /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \       /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \            /                                                    ________                                                   \           /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \                         /                                                    ________                                                   \                     /                                                    ________                                                   \                                                                                                              /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \     /                                                            ________                     \ /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \     /                                                    ________                                                   \ |        ________                                        ________                                                                                                                                      ________                             ________                                                 /                           2                                               \   10*x *log (x)*|- ----------- + --------|             ________                                              ________                                     |      /                                                    ________                                                   \ /                                                            ________                     \      /                                                    ________                                                   \                                                                                                                  /                                                    ________                                                   \ /                                                            ________                     \      /                                                    ________                                                   \ /                                                            ________                     \         /                                                    ________                                                   \                                                                                                               /                                                    ________                                                   \                                                                                                                    /                                                    ________                                                   \   /                                                    ________                                                   \                                                                                                          /                                                            ________                     \                      /                                                    ________                                                   \          /                                                    ________                                                   \                                                                                                                  /                                                    ________                                                   \ /                                                            ________                     \                     /                                       ________                                                                                                                                                  ________                                                             ________                                                                ________                                                              ________         /                          2                                                                                \                                                                      ________                                                                  \                          /                                                    ________                                                   \                    /                                                    ________                                                   \ /                                                            ________                     \                    /                                                    ________                                                   \                                                                                                         |
                              |          |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |       |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |           |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |             |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |           |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |           |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |        |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |        |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |                     |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |      |       3    2           3    3           13    3           3            /         2           3  \ |      9    2           /      5                     4              4    2          4                    |                    /     ________                   5       \ |              /       2   \            6          2         3 /       2   \|        /      5  /        2   \        8    2           8    3           3                           3    2                                   |   /     5\                                       /      5        /      5              /      5        |              8    2                         |   /     5\                                       /      5        /      5              /      5        |               /      5     3    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |        /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |         3   /      5     2    /  /       2   \ /       4\       3       \         3   /      5     3    /  /       2   \ /       4\       3       \         8    3    /  /       2   \ /       4\       3       \         4   /      5     3    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       9    3    /  /       2   \ /       4\       3       \          /      5     3    |  /       2   \  /       4\           9                6 /       2   \ /       4\        2 /       4\  /       2   \     /       4\     2    /       2   \         /       4\                 5 /       4\               3 /       4\  /       2   \       |        /      5     2    /  /       2   \ /       4\       3       \        /      5     3    /       2   \ /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \              5    3    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |        /      5     2    /       2   \ /  /       2   \ /       4\       3       \        4    2    /  /       2   \ /       4\       3       \        4    3    /  /       2   \ /       4\       3       \          7   /      5     3    /  /       2   \ /       4\       3       \         4   /      5     3    /       2   \ /  /       2   \ /       4\       3       \          /      5     3    /       2   \ /  /       2   \ /       4\       3       \        /       2   \    /      5     3    /  /       2   \ /       4\       3       \          /      5     3    /       2   \ |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    3    /       2   \ /  /       2   \ /       4\       3       \|       |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|          |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|       |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|            |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |           |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|                         |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |                     |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |     /     ________        ________             5                 ________ /         2           3  \       \ |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|     |     ________        ________             5                /      5  /       2   \       | |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|     |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |       /      5        4    2          4               /      5                ________         /         2           3  \         ________ /         2           3  \              9    2           /      5  /       2   \              /      5     2    /       2   \          ________         |              /       2   \            6          2         3 /       2   \|                 |     cot(x)            4|        3   /      5     2               8    2               3   /      5               5    2    /       2   \|      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |     ________        ________             5                /      5  /       2   \       |      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \         |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |     ________        ________             5                /      5  /       2   \       |      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |     ________        ________             5                /      5  /       2   \       |         |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \           |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |   |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \ |     ________        ________             5                /      5  /       2   \       |                      |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |          |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \         |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |     ________        ________             5                /      5  /       2   \       |                     |      4    2          4               /      5                   /         2           3  \ /     ________                   5       \              9    2          4                           /      5     2    /  /       2   \ /       4\       3       \        /      5  /  /       2   \ /       4\       3       \               4   /      5     2    /  /       2   \ /       4\       3       \         /      5     2    |     6          /       4\  /       2   \              3 /       2   \ /       4\       2 /       4\       |       5    2    /  /       2   \ /       4\       3       \         /      5     2    /       2   \ /  /       2   \ /       4\       3       \|                          |       ________                   5                /      5  /  /       2   \ /       4\       3       \       |                    |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | |     ________        ________             5                /      5  /       2   \       |                    |       ________                   5                /      5  /  /       2   \ /       4\       3       \       | /     ________        ________             5                 ________ /         2           3  \       \|
                              |        7 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|       |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|         2 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|           5 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|           |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|         2 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|        |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|        |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|       /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|      |  540*x *log (x)   400*x *log (x)   375*x  *log (x)   120*x *log(x)     |  1 + cot (x)    40*x   | |  25*x *log (x)   12*\/  9 + x  *(2 + log(x))   30*x *log(x)   50*x *log (x)   10*x *(3 + log(x))*log(x)|               2    |    /      5                 5*x *log(x)| |       2      \1 + cot (x)/       960*x       60*x      40*x *\1 + cot (x)/|   24*\/  9 + x  *\-2 + log (x)/   300*x *log (x)   700*x *log (x)   120*x *(2 + log(x))*log(x)   80*x *log (x)*(3 + log(x))                   \   \9 + x /                                     \/  9 + x       \/  9 + x             \/  9 + x         /          50*x *log (x)*(3 + log(x))         \   \9 + x /                                     \/  9 + x       \/  9 + x             \/  9 + x         /          32*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   96*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   3840*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   3200*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   3200*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   2560*x *\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   50*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   16*x*\/  9 + x  *log (x)*\- \1 + cot (x)/ *\5 + 2*x /  + 15360*x *cot(x) - 1920*x *\1 + cot (x)/*\5 + 2*x / - 180*x *\5 + 2*x / *\1 + cot (x)/ - 2*\5 + 2*x / *cot (x)*\1 + cot (x)/ + 120*x*\5 + 2*x / *cot(x) + 5760*x *\5 + 2*x /*cot(x) + 120*x *\5 + 2*x / *\1 + cot (x)/*cot(x)/   24*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   32*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   48*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   80*x *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   96*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   120*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   120*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   56320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   2560*x *\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   32*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   48*x*\1 + cot (x)/ *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   64*x*\/  9 + x  *log (x)*\1 + cot (x)/*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   80*x *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|       |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|        3 |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|       |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|          6 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|         2 |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|         3 /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|       /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|     |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       | |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|     |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)| |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|     |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |  24*\/  9 + x     60*x *log (x)   60*x *log(x)   12*\/  9 + x  *log(x)       /      5     2    |  1 + cot (x)    40*x   |        /      5  |  1 + cot (x)    40*x   |          25*x *log (x)   12*\/  9 + x  *\1 + cot (x)/*log(x)   4*\/  9 + x  *log (x)*\1 + cot (x)/         /      5     2    |       2      \1 + cot (x)/       960*x       60*x      40*x *\1 + cot (x)/|                 \                5 + 2*x /   160*x *\/  9 + x  *log (x)       400*x *log (x)       480*x *\/  9 + x  *log(x)   10*x *log (x)*\1 + cot (x)/|      |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|      |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       |       2 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|      |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|       2 |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       |      |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       |           |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|   |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       | |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|        /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|          |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       |         |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|       /       2   \ |  50*x *log (x)   30*x *log(x)   12*\/  9 + x  *(2 + log(x))     |  1 + cot (x)    40*x   | |    /      5                 5*x *log(x)|          25*x *log (x)   10*x *(3 + log(x))*log(x)   4*\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   12*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)   320*x *\/  9 + x  *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\640*x *cot(x) + \5 + 2*x / *\1 + cot (x)/*cot(x) - 40*x *\1 + cot (x)/*\5 + 2*x / + 60*x *\5 + 2*x /*cot(x)/   10*x *log (x)*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/   8*x*\/  9 + x  *log (x)*\1 + cot (x)/*\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/|          2 /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)|      /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)   2*x*\/  9 + x  *\1 + cot (x)/*log(x)|      /       2   \ |      /      5                 5*x *log(x)   2*x*\/  9 + x  *\- \1 + cot (x)/*\5 + 2*x / + 40*x *cot(x)/*log(x)| |    /      5        /      5           5*x *log(x)         /      5  |  1 + cot (x)    40*x   |       ||
      _______________________ |  4800*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   512*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   1280*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   276480*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   11520*x*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   3840*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   3072*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   2304*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   512*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   64*|- -------------- - -------------- - --------------- - ------------- + 2*|- ----------- + --------|*|- ------------- + --------------------------- + ------------ + ------------- + -------------------------|*log(x) + 8*log (x)*|2*\/  9 + x  *(3 + log(x)) + -----------|*|1 + cot (x) - -------------- - ----------- + -------- + -------------------| + ----------------------------- + -------------- + -------------- - -------------------------- - -------------------------- - --------------------------------------------------------------------------------------------------------------------------------- + -------------------------- + ----------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------- - ----------------------------------------------------------------------- - ----------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------------------------------------------- + ----------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + ---------------------------------------------------------- + ---------------------------------------------------------- + ------------------------------------------------------------------------ - ------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------|   256*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   640*x *|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   768*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   48000*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   9600*x *|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   1280*x *\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   512*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   8*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   8*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   8*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|- -------------- - ------------- - ------------ - --------------------- + 4*\/  9 + x  *log (x)*|- ----------- + --------| + 12*\/  9 + x  *|- ----------- + --------|*log(x) + ------------- - ----------------------------------- - ----------------------------------- + 8*x*\/  9 + x  *log (x)*|1 + cot (x) - -------------- - ----------- + -------- + -------------------| + ---------------------------------------- + -------------------------- + ---------------------- + ------------------------- - ---------------------------|   16*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   32*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|   40*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   48*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   80*x *|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|   96*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|   57600*x*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   |- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   1536*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   1200*x*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)|   640*x*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   256*\1 + cot (x)/*|- ------------- - ------------ - --------------------------- + 2*|- ----------- + --------|*|2*\/  9 + x  *(3 + log(x)) + -----------|*log(x) + ------------- - ------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------- + ---------------------------------------------------------------------------------|   19200*x *\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|   16*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- + ------------------------------------|   32*\1 + cot (x)/*|- 2*\/  9 + x  *(3 + log(x)) - ----------- + ------------------------------------------------------------------|*|6*\/  9 + x   + 2*\/  9 + x  *log(x) + ----------- - 2*x*\/  9 + x  *|- ----------- + --------|*log(x)||
     /      ________          |          |                                  ________                           /       4\                                |       |                                  ________                           /       4\                                |           |                                  ________                           /       4\                                |             |                                  ________                           /       4\                                |           |                                  ________                           /       4\                                |           |                                  ________                           /       4\                                |        |                                  ________                           /       4\                                |        |                                  ________                           /       4\                                |                     |                                  ________                           /       4\                                |      |      ________         ________               5/2         ________      |     cot(x)            4| |           3/2                 x                   ________        ________              ________       |                    |                                ________| |                    2                    2          4    /       4\        |                  2                         3/2              3/2               ________                     ________                                                                         cot(x)                                                                               3/2                                                                          4                                                                                                                             2                                                                                                                                      2                                                                                                        2                                                                         2                                                             2    ________                                                                                              3                                                                                                      3/2                                                                                                                                                                    3                                                                                                                                                                     /       4\                                                                 /       4\    2                                                              /       4\                                                                                          2    ________                                                                                       /       4\    2                                                                 ________                                                     ________                                                              3                                                                                2                                                                            /       4\                                                                            /       4\    3                                                                                                                2                                                                                                               ________                            |       |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |          |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |       |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |            |                                  ________                           /       4\                                |           |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |                         |                                  ________                           /       4\                                |                     |                                  ________                           /       4\                                |     |                                          ________                   |     cot(x)            4|       | |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |     |                                          ________                  cot(x)               | |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |     |                                  ________                           /       4\                                | |        x              ________       ________              x                                   |     cot(x)            4|                  |     cot(x)            4|                   3/2                   cot(x)                                cot(x)                                         |                    2                    2          4    /       4\        |                    ________                                  4                          ________                   4                   ________           |      |                                  ________                           /       4\                                | |                                          ________                  cot(x)               |      |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       |         |                                  ________                           /       4\                                | |                                          ________                  cot(x)               |      |                                  ________                           /       4\                                | |                                          ________                  cot(x)               |         |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       |      |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       |           |                                  ________                           /       4\                                |   |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       | |                                          ________                  cot(x)               |                      |                                  ________                           /       4\                                |          |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       |         |                                  ________                           /       4\                                | |                                          ________                  cot(x)               |                     |      ________       ________                 x                  |     cot(x)            4| |                                ________|                   3/2              ________                                  /       4\                                                          /       4\                                                                      2                                                                                                        2                                                                                               ________                                                        /       4\    2                                  |                          |                                  ________                           /       4\                                |                    |                                  ________                           /       4\                                | |                                          ________                  cot(x)               |                    |                                  ________                           /       4\                                | |                                          ________                   |     cot(x)            4|       ||
    /      /      5     3     |          |                                 /      5                            \5 + 2*x /*cot(x)                         |       |                                 /      5                            \5 + 2*x /*cot(x)                         |           |                                 /      5                            \5 + 2*x /*cot(x)                         |             |                                 /      5                            \5 + 2*x /*cot(x)                         |           |                                 /      5                            \5 + 2*x /*cot(x)                         |           |                                 /      5                            \5 + 2*x /*cot(x)                         |        |                                 /      5                            \5 + 2*x /*cot(x)                         |        |                                 /      5                            \5 + 2*x /*cot(x)                         |                     |                                 /      5                            \5 + 2*x /*cot(x)                         |      |     /      5         /      5        /     5\           /      5       \                5 + 2*x / |   /     5\                                       /      5        /      5              /      5        |                    |                               /      5 | |                 cot (x)       /       4\    5 + 2*x     \5 + 2*x /*cot(x) |                 x                  /     5\         /     5\                 /      5                     /      5                                                                                                                                                       /     5\                                                                      5 + 2*x                                                                                                                    /       4\                                                                                                                             /       4\                                                                                               /       4\                                                                /       4\                                                    /       4\    /      5                                                                                     /       4\                                                                                    /       4\ /     5\                                                                                                                                                             /       4\                                                                                                                                                                    x*\5 + 2*x /*cot(x)                                                          \5 + 2*x /*cot (x)                                                         x*\5 + 2*x /*cot(x)                                                                         /       4\    /      5                                                                                        \5 + 2*x /*cot (x)                                                /       4\   /      5                                        /       4\   /      5                                                     /       4\                                                                       /       4\     2                                                                       \5 + 2*x /*cot(x)                                                                     \5 + 2*x /*cot (x)                                                                                                   /       4\     2                                                                                            /       4\   /      5     2                       |       |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |          |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |       |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |            |                                 /      5                            \5 + 2*x /*cot(x)                         |           |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |                         |                                 /      5                            \5 + 2*x /*cot(x)                         |                     |                                 /      5                            \5 + 2*x /*cot(x)                         |     |                                         /      5                    \                5 + 2*x /       | |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |     |                                         /      5                                        | |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |     |                                 /      5                            \5 + 2*x /*cot(x)                         | |                      /      5       /      5                                                   \                5 + 2*x /                  \                5 + 2*x /           /     5\                                                                                                           |                 cot (x)       /       4\    5 + 2*x     \5 + 2*x /*cot(x) |                   /      5                            5 + 2*x             /       4\   /      5             5 + 2*x                   /      5            |      |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                                        |      |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       |         |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                                        |      |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                                        |         |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       |      |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       |           |                                 /      5                            \5 + 2*x /*cot(x)                         |   |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       | |                                         /      5                                        |                      |                                 /      5                            \5 + 2*x /*cot(x)                         |          |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       |         |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                                        |                     |     /      5       /      5                                     \                5 + 2*x / |                               /      5 |           /     5\                /      5                                   \5 + 2*x /*cot(x)                                                   \5 + 2*x /*cot(x)                                                     /       4\                                                                                               /       4\                                                                                  /       4\   /      5                                                         \5 + 2*x /*cot (x)                               |                          |                                 /      5                            \5 + 2*x /*cot(x)                         |                    |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                                        |                    |                                 /      5                            \5 + 2*x /*cot(x)                         | |                                         /      5                    \                5 + 2*x /       ||
   /   x*\/  9 + x  *log (x)  |          \                               \/  9 + x                                                                       /       \                               \/  9 + x                                                                       /           \                               \/  9 + x                                                                       /             \                               \/  9 + x                                                                       /           \                               \/  9 + x                                                                       /           \                               \/  9 + x                                                                       /        \                               \/  9 + x                                                                       /        \                               \/  9 + x                                                                       /                     \                               \/  9 + x                                                                       /      \   \/  9 + x        \/  9 + x         \9 + x /         \/  9 + x                                   \   \9 + x /                                     \/  9 + x       \/  9 + x             \/  9 + x         /                    \                             \/  9 + x  / \                               \5 + 2*x /                                  /                                    \9 + x /         \9 + x /               \/  9 + x                    \/  9 + x                                                                                                                                                        \9 + x /                                                                                                                                                                                                 \5 + 2*x / *cot(x)                                                                                                                     \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                        \5 + 2*x / *cot(x)                                            \5 + 2*x / *\/  9 + x  *cot(x)                                                                             \5 + 2*x / *cot(x)                                                                            \5 + 2*x /*\9 + x /   *cot(x)                                                                                                                                                   \5 + 2*x / *cot(x)                                                                                                                                                                                                                                                                                                                                                                                                                \5 + 2*x / *\/  9 + x  *cot(x)                                                                                                                                                  \5 + 2*x /*\/  9 + x  *cot(x)                                \5 + 2*x /*\/  9 + x  *cot(x)                                             \5 + 2*x / *cot(x)                                                               \5 + 2*x / *cot (x)                                                                                                                                                                                                                                                                               \5 + 2*x / *cot (x)                                                                                         \5 + 2*x /*\/  9 + x  *cot (x)                    /       \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /          \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /       \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /            \                               \/  9 + x                                                                       /           \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /                         \                               \/  9 + x                                                                       /                     \                               \/  9 + x                                                                       /     \                                       \/  9 + x                                                      / \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /     \                                       \/  9 + x                                         / \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /     \                               \/  9 + x                                                                       / \                    \/  9 + x      \/  9 + x                                                                                                                                     \9 + x /                                                                                                           \                               \5 + 2*x /                                  /                 \/  9 + x                                                 \5 + 2*x /*\/  9 + x                                      \/  9 + x  *cot(x)    /      \                               \/  9 + x                                                                       / \                                       \/  9 + x                                         /      \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /         \                               \/  9 + x                                                                       / \                                       \/  9 + x                                         /      \                               \/  9 + x                                                                       / \                                       \/  9 + x                                         /         \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /      \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /           \                               \/  9 + x                                                                       /   \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      / \                                       \/  9 + x                                         /                      \                               \/  9 + x                                                                       /          \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /         \                               \/  9 + x                                                                       / \                                       \/  9 + x                                         /                     \   \/  9 + x      \/  9 + x                                                                 \                             \/  9 + x  /           \9 + x /              \/  9 + x                                                                                                                                                                              \5 + 2*x / *cot(x)                                                                                       \5 + 2*x / *cot(x)                                                                          \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                  /                          \                               \/  9 + x                                                                       /                    \                               \/  9 + x                                                                       / \                                       \/  9 + x                                         /                    \                               \/  9 + x                                                                       / \                                       \/  9 + x                                                      /|
8 /    --------------------- *|- ------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- - 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+ -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 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------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------- - 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----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ - 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\/             cot(x)         |                                                                 5/2                                                                                                                    ________                                                                                                                     3/2                                                                                                                      2    ________                                                                                                                     ________                                                                                                                3/2                                                                                                                   ________                                                                                                                 ________                                                                                                                           ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         3/2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     ________                                                                                                                                                                                                                                                                                                                                                                                                                         3/2                                                                                                                                                                                                                                                                                                                                                                                                          ________                                                                                                                                                                                                                                                                                                                                                                                                                     3/2                                                                                                                                 ________                                                                                                                                                                                                                                                                                                                                                                                                                                                                2 /     5\    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2 /     5\    2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2 /     5\    2                                                                                                                                                                                                                                                                                                                                                                                                                              3 /     5\                                                                                                                                                                                                                3 /     5\                                                                                                                                                                                                                         2                                                                                                                                                                                                          3 /     5\    2                                                                                                                                                                                                                     2                                                                                                                                                                                                                        3 /     5\    2                                                                                                                                                                       ________                                                                                                                                                                                                                   3/2                                                                                                                                                                                                                     ________                                                                                                                                                                         /       4\ /     5\                                                                                                                                                                                                          /       4\ /     5\                                                                                                                                                                                                                                                                                                                                                                                                                                                        ________                                                                                                                                                                                                                                                                                                                                                                                                                                  ________                                                                                                                                                                   2 /     5\                                                                                                                                                                                                                              2 /     5\                                                                                                                       |
                              |                                                         /     5\                                                                                                                  3   /      5                                                                                                              /     5\                                                                                                               /       4\    /      5                                                                                                        /       4\   /      5                                                                                                         /     5\                                                                                                                 3   /      5     2                                                                                                       3   /      5                                                                                                                           /      5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              /      5     2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2   /      5                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /     5\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2   /      5     2                                                                                                                                                                                                                                                                                                                                                                                                 /       4\ /     5\                                                                                                                                                                                                                                                                                                                                                                                               /       4\   /      5                                                                                                                                                                                                                                                                                                                                                                                                              /     5\                                                                                                                               2   /      5                                                                                                                                                                                                                                                                                                                                                                                                                                                                x *\9 + x /*log (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        x *\9 + x /*log (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  x *\9 + x /*log (x)                                                                                                                                                                                                                                                                                                                                                                                                                          x *\9 + x /*log(x)                                                                                                                                                                                                        x *\9 + x /*log(x)                                                                                                                                                                                                          /     5\                                                                                                                                                                                                          x *\9 + x /*log (x)                                                                                                                                                                                                          /     5\                                                                                                                                                                                                                        x *\9 + x /*log (x)                                                                                                                                                      /       4\   /      5                                                                                                                                                                                                          3 /     5\       2                                                                                                                                                                                                           2   /      5                                                                                                                                                                          \5 + 2*x /*\9 + x /*log(x)                                                                                                                                                                                                   \5 + 2*x /*\9 + x /*log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                /      5                                                                                                                                                                                                                                                                                                                                                                                                                     /       4\   /      5                                                                                                                                                                   x *\9 + x /*cot(x)*log(x)                                                                                                                                                                                                               x *\9 + x /*cot(x)*log(x)                                                                                                         |
                              \                                                         \9 + x /                                                                                                                 x *\/  9 + x                                                                                                               \9 + x /                                                                                                               \5 + 2*x / *\/  9 + x                                                                                                         \5 + 2*x /*\/  9 + x                                                                                                          \9 + x /   *log(x)                                                                                                      x *\/  9 + x  *log (x)                                                                                                   x *\/  9 + x  *log(x)                                                                                                               x*\/  9 + x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           x*\/  9 + x  *log (x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        x *\/  9 + x  *log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \9 + x /   *log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        x *\/  9 + x  *log (x)                                                                                                                                                                                                                                                                                                                                                                                              \5 + 2*x /*\9 + x /                                                                                                                                                                                                                                                                                                                                                                                               \5 + 2*x /*\/  9 + x  *log(x)                                                                                                                                                                                                                                                                                                                                                                                                      \9 + x /   *cot(x)                                                                                                                    x *\/  9 + x  *cot(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           \9 + x / *log(x)                                                                                                                                                                                                                                                                                                                                                                                                                               \9 + x / *log(x)                                                                                                                                                                                                                                                                                                                                                                                         \5 + 2*x /*\/  9 + x  *log(x)                                                                                                                                                                                                 x *\9 + x /   *log (x)                                                                                                                                                                                                       x *\/  9 + x  *cot(x)*log(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              x*\/  9 + x  *cot(x)*log(x)                                                                                                                                                                                                                                                                                                                                                                                                      \5 + 2*x /*\/  9 + x  *cot(x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        5/8                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /       4\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           4096*\5 + 2*x /   *log(x)

$$\frac{\sqrt[8]{\frac{x \sqrt{x^{5} + 9} \log{\left(x \right)}^{3}}{\cot{\left(x \right)}}} \left(- \frac{4800 x^{7} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(x^{5} + 9\right)^{\frac{5}{2}}} + \frac{48000 x^{6} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right) \left(x^{5} + 9\right)^{\frac{3}{2}}} - \frac{276480 x^{5} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right)^{2} \sqrt{x^{5} + 9}} - \frac{1280 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(x^{5} + 9\right)^{\frac{3}{2}} \cot{\left(x \right)}} + \frac{640 x^{3} \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{\left(x^{5} + 9\right)^{\frac{3}{2}} \log{\left(x \right)}} + \frac{80 x^{2} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{\left(x^{5} + 9\right)^{2} \log{\left(x \right)}} + \frac{40 x^{2} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{\left(x^{5} + 9\right)^{2} \log{\left(x \right)}} + \frac{1280 x^{2} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(x^{5} + 9\right)^{\frac{3}{2}}} - \frac{3840 x^{2} \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(x^{5} + 9\right)^{\frac{3}{2}} \log{\left(x \right)}} + \frac{19200 x^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{9600 x^{2} \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \log{\left(x \right)}} - \frac{1200 x \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{\left(2 x^{4} + 5\right) \left(x^{5} + 9\right) \log{\left(x \right)}} - \frac{640 x \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{\left(2 x^{4} + 5\right) \left(x^{5} + 9\right) \log{\left(x \right)}} - \frac{11520 x \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9}} + \frac{57600 x \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \log{\left(x \right)}} - \frac{512 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x \sqrt{x^{5} + 9}} + \frac{256 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x \sqrt{x^{5} + 9} \log{\left(x \right)} \cot{\left(x \right)}} - \frac{64 \left(- \frac{375 x^{13} \log{\left(x \right)}^{3}}{\left(x^{5} + 9\right)^{\frac{5}{2}}} - \frac{50 x^{9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \left(x^{5} + 9\right)^{\frac{3}{2}} \cot{\left(x \right)}} + \frac{50 x^{8} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{700 x^{8} \log{\left(x \right)}^{3}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{300 x^{8} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} - \frac{3200 x^{8} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \sqrt{x^{5} + 9} \cot{\left(x \right)}} + \frac{56320 x^{7} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{3} \cot{\left(x \right)}} + \frac{80 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot^{2}{\left(x \right)}} + \frac{80 x^{5} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \sqrt{x^{5} + 9} \cot{\left(x \right)}} + \frac{120 x^{4} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} + \frac{120 x^{4} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{2560 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \cot^{2}{\left(x \right)}} - \frac{2560 x^{4} \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{3} \cot{\left(x \right)}} - \frac{120 x^{3} \left(\log{\left(x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{80 x^{3} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{400 x^{3} \log{\left(x \right)}^{3}}{\sqrt{x^{5} + 9}} - \frac{540 x^{3} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{120 x^{3} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{80 x^{3} \left(- \frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} + \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right) \log{\left(x \right)}}{2 x^{4} + 5} - \frac{3200 x^{3} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} - \frac{3840 x^{3} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{48 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \cot^{3}{\left(x \right)}} - \frac{32 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{64 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \cot^{2}{\left(x \right)}} + \frac{16 x \sqrt{x^{5} + 9} \left(15360 x^{9} \cot{\left(x \right)} - 1920 x^{6} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 5760 x^{5} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + 120 x^{3} \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - 180 x^{2} \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) + 120 x \left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)} - \left(2 x^{4} + 5\right)^{3} \left(\cot^{2}{\left(x \right)} + 1\right)^{2} - 2 \left(2 x^{4} + 5\right)^{3} \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{3} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(- \frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} + \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right) \log{\left(x \right)} + 8 \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(- \frac{960 x^{6}}{\left(2 x^{4} + 5\right)^{2}} + \frac{40 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{60 x^{2}}{2 x^{4} + 5} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + \cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} + \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + \frac{32 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{96 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{32 \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{3}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{96 \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{24 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{x \left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{48 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{x \left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{24 \sqrt{x^{5} + 9} \left(\log{\left(x \right)}^{2} - 2\right)}{x^{2}}\right)}{x \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}} + \frac{32 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)} \cot{\left(x \right)}} + \frac{16 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)} \cot{\left(x \right)}} + \frac{8 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{400 x^{8} \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9}} + \frac{10 x^{5} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{10 x^{5} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{60 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{60 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{160 x^{3} \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}}{2 x^{4} + 5} + \frac{480 x^{3} \sqrt{x^{5} + 9} \log{\left(x \right)}}{2 x^{4} + 5} + 8 x \sqrt{x^{5} + 9} \left(- \frac{960 x^{6}}{\left(2 x^{4} + 5\right)^{2}} + \frac{40 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{60 x^{2}}{2 x^{4} + 5} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + \cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2} + 4 \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)}^{2} + 12 \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} - \frac{4 \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \log{\left(x \right)}}{x} - \frac{24 \sqrt{x^{5} + 9}}{x}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)}^{2}} - \frac{8 \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right) \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)}^{2}} - \frac{8 \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right) \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x^{2} \left(x^{5} + 9\right) \log{\left(x \right)}^{2}} - \frac{512 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{2} \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{1536 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{2} \sqrt{x^{5} + 9} \log{\left(x \right)} \cot{\left(x \right)}} + \frac{256 \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x^{2} \sqrt{x^{5} + 9} \log{\left(x \right)}} + \frac{768 \left(\frac{25 x^{9} \log{\left(x \right)}^{2}}{\left(x^{5} + 9\right)^{\frac{3}{2}}} + \frac{10 x^{5} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \sqrt{x^{5} + 9} \cot{\left(x \right)}} - \frac{10 x^{4} \left(\log{\left(x \right)} + 3\right) \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{50 x^{4} \log{\left(x \right)}^{2}}{\sqrt{x^{5} + 9}} - \frac{30 x^{4} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - \frac{320 x^{4} \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot^{2}{\left(x \right)}} + \frac{8 x \sqrt{x^{5} + 9} \left(640 x^{6} \cot{\left(x \right)} - 40 x^{3} \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 60 x^{2} \left(2 x^{4} + 5\right) \cot{\left(x \right)} + \left(2 x^{4} + 5\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right)^{2} \cot{\left(x \right)}} + 2 \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \log{\left(x \right)} + \frac{4 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}^{2}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} + \frac{12 \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - \frac{12 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 2\right)}{x}\right)}{x^{2} \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}} + \frac{32 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{3} \left(x^{5} + 9\right) \log{\left(x \right)}} + \frac{96 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{3} \left(x^{5} + 9\right) \log{\left(x \right)}^{2}} + \frac{16 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{3} \left(x^{5} + 9\right) \log{\left(x \right)}} + \frac{48 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{3} \left(x^{5} + 9\right) \log{\left(x \right)}^{2}} - \frac{512 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{3} \sqrt{x^{5} + 9}} - \frac{2304 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{3} \sqrt{x^{5} + 9} \log{\left(x \right)}} - \frac{3072 \left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right)}{x^{3} \sqrt{x^{5} + 9} \log{\left(x \right)}^{2}} - \frac{\left(- \frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(40 x^{3} \cot{\left(x \right)} - \left(2 x^{4} + 5\right) \left(\cot^{2}{\left(x \right)} + 1\right)\right) \log{\left(x \right)}}{\left(2 x^{4} + 5\right) \cot{\left(x \right)}} - 2 \sqrt{x^{5} + 9} \left(\log{\left(x \right)} + 3\right)\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} - 2 x \sqrt{x^{5} + 9} \left(\frac{40 x^{3}}{2 x^{4} + 5} - \frac{\cot^{2}{\left(x \right)} + 1}{\cot{\left(x \right)}}\right) \log{\left(x \right)} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right) \left(\frac{5 x^{5} \log{\left(x \right)}}{\sqrt{x^{5} + 9}} + \frac{2 x \sqrt{x^{5} + 9} \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\cot{\left(x \right)}} + 2 \sqrt{x^{5} + 9} \log{\left(x \right)} + 6 \sqrt{x^{5} + 9}\right)}{x^{3} \left(x^{5} + 9\right)^{\frac{3}{2}} \log{\left(x \right)}^{2}}\right)}{4096 \left(2 x^{4} + 5\right)^{\frac{5}{8}} \log{\left(x \right)}}$$

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Gráfico

Derivada de ((xln^3(x)sqrt(x^5+9))/(ctgx(2x^4+5)^5))^(1/8)

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Derivada de ((xln^3(x)sqrt(x^5+9))/(ctgx(2x^4+5)^5))^(1/8)

Gráfico:

Definida a trozos:

Solución

Method #1

Method #2