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(2x-1)/(x*(x+2)^2*(x-4))
((x+1)^2*(8*x-4))^(1/3)*(8*(x+1)^2/3+(2+2*x)*(8*x-4)/3)/((x+1)^2*(8*x-4))
((z+p)/(2*(z-p)))-((z-p)/(2*(z+p)))-((p)/(z-p))
-z^3-(-1)*z^(2*y)*(-x)*z/(z^2+x*y)-y^(2*x)*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
Factorizar el polinomio:
z^3-6*z^2+5*z+12
z^2*x^2-9*y*y^2/100
z^2/2-2*i*z
x^4+x^2
Descomponer al cuadrado:
-y^4+y^2-5
y^4+y^2-4
y^4-3*y^2-1
-y^2+4*y+3
Expresiones idénticas
sqrt(sin(x)+ uno)*(- tres *x^ dos + tres *sin(x))/(x^ tres + tres *cos(x))^ dos +cos(x)/(dos *(x^ tres + tres *cos(x))*sqrt(sin(x)+ uno))
raíz cuadrada de ( seno de (x) más 1) multiplicar por ( menos 3 multiplicar por x al cuadrado más 3 multiplicar por seno de (x)) dividir por (x al cubo más 3 multiplicar por coseno de (x)) al cuadrado más coseno de (x) dividir por (2 multiplicar por (x al cubo más 3 multiplicar por coseno de (x)) multiplicar por raíz cuadrada de ( seno de (x) más 1))
raíz cuadrada de ( seno de (x) más uno) multiplicar por ( menos tres multiplicar por x en el grado dos más tres multiplicar por seno de (x)) dividir por (x en el grado tres más tres multiplicar por coseno de (x)) en el grado dos más coseno de (x) dividir por (dos multiplicar por (x en el grado tres más tres multiplicar por coseno de (x)) multiplicar por raíz cuadrada de ( seno de (x) más uno))
√(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*√(sin(x)+1))
sqrt(sin(x)+1)*(-3*x2+3*sin(x))/(x3+3*cos(x))2+cos(x)/(2*(x3+3*cos(x))*sqrt(sin(x)+1))
sqrtsinx+1*-3*x2+3*sinx/x3+3*cosx2+cosx/2*x3+3*cosx*sqrtsinx+1
sqrt(sin(x)+1)*(-3*x²+3*sin(x))/(x³+3*cos(x))²+cos(x)/(2*(x³+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)*(-3*x en el grado 2+3*sin(x))/(x en el grado 3+3*cos(x)) en el grado 2+cos(x)/(2*(x en el grado 3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)(-3x^2+3sin(x))/(x^3+3cos(x))^2+cos(x)/(2(x^3+3cos(x))sqrt(sin(x)+1))
sqrt(sin(x)+1)(-3x2+3sin(x))/(x3+3cos(x))2+cos(x)/(2(x3+3cos(x))sqrt(sin(x)+1))
sqrtsinx+1-3x2+3sinx/x3+3cosx2+cosx/2x3+3cosxsqrtsinx+1
sqrtsinx+1-3x^2+3sinx/x^3+3cosx^2+cosx/2x^3+3cosxsqrtsinx+1
sqrt(sin(x)+1)*(-3*x^2+3*sin(x)) dividir por (x^3+3*cos(x))^2+cos(x) dividir por (2*(x^3+3*cos(x))*sqrt(sin(x)+1))
Expresiones semejantes
sqrt(sin(x)+1)*(3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)*(-3*x^2-3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3-3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)-1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)-1))
sqrt(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2-cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))
sqrt(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3-3*cos(x))*sqrt(sin(x)+1))
sqrt(sinx+1)*(-3*x^2+3*sinx)/(x^3+3*cosx)^2+cosx/(2*(x^3+3*cosx)*sqrt(sinx+1))
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2))
sqrt(x)/sqrt(1-x^2)+asin(x)/(2*sqrt(x))
sqrt(x+2)*(13/10-3*x/5)+(19/5+13*x/10-3*x^(1/5))/(2*sqrt(x+2))
sqrt(81*b^(1/7))/(b^(1/14))еслиb=5
sqrt(2)/(sqrt(8)+2)-(6-sqrt(32))/sqrt(8)-3
Seno sin
sin40/(2*cos20)
sin(2nx)/(2n)-cos(2nx)/(4n^2)
sin(2*x)/(2*sin(x)-cos(x))
sin(2*x)/(2*cos(2*x))
sin(x)/(2*sqrt(1-cos(x)^2)*sqrt(acos(cos(x))))
Seno sin
sin40/(2*cos20)
sin(2nx)/(2n)-cos(2nx)/(4n^2)
sin(2*x)/(2*sin(x)-cos(x))
sin(2*x)/(2*cos(2*x))
sin(x)/(2*sqrt(1-cos(x)^2)*sqrt(acos(cos(x))))
Coseno cos
cos(3*x)/((3*x))
cos(5)/((4*x))
cos(a-b)/((sin(a)*sin(b)))-1
cos(2*x)/(sin(x)-cos(x))
cos(x)/(2*sqrt(1+sin(x)))
Coseno cos
cos(3*x)/((3*x))
cos(5)/((4*x))
cos(a-b)/((sin(a)*sin(b)))-1
cos(2*x)/(sin(x)-cos(x))
cos(x)/(2*sqrt(1+sin(x)))
Coseno cos
cos(3*x)/((3*x))
cos(5)/((4*x))
cos(a-b)/((sin(a)*sin(b)))-1
cos(2*x)/(sin(x)-cos(x))
cos(x)/(2*sqrt(1+sin(x)))
Raíz cuadrada sqrt
sqrt(675+30*x-x^2)/4+(15+x)*(15-x)/(4*sqrt(675+30*x-x^2))
sqrt(x)/sqrt(1-x^2)+asin(x)/(2*sqrt(x))
sqrt(x+2)*(13/10-3*x/5)+(19/5+13*x/10-3*x^(1/5))/(2*sqrt(x+2))
sqrt(81*b^(1/7))/(b^(1/14))еслиb=5
sqrt(2)/(sqrt(8)+2)-(6-sqrt(32))/sqrt(8)-3
Seno sin
sin40/(2*cos20)
sin(2nx)/(2n)-cos(2nx)/(4n^2)
sin(2*x)/(2*sin(x)-cos(x))
sin(2*x)/(2*cos(2*x))
sin(x)/(2*sqrt(1-cos(x)^2)*sqrt(acos(cos(x))))

Simplificación de expresiones/ Descomposición en fracciones simples/ sqrt(sin(x)+1)*(-3*x^2+3*sin(x))/(x^3+3*cos(x))^2+cos(x)/(2*(x^3+3*cos(x))*sqrt(sin(x)+1))

¿Cómo vas a descomponer esta sqrt(sin(x)+1)(-3x^2+3sin(x))/(x^3+3cos(x))^2+cos(x)/(2(x^3+3cos(x))*sqrt(sin(x)+1)) expresión en fracciones?

Solución

Ha introducido [src]

  ____________ /     2           \                                   
\/ sin(x) + 1 *\- 3*x  + 3*sin(x)/                cos(x)             
---------------------------------- + --------------------------------
                        2              / 3           \   ____________
         / 3           \             2*\x  + 3*cos(x)/*\/ sin(x) + 1 
         \x  + 3*cos(x)/

\frac{\left(- 3 x^{2} + 3 \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

(sqrt(sin(x) + 1)*(-3*x^2 + 3*sin(x)))/(x^3 + 3*cos(x))^2 + cos(x)/(((2*(x^3 + 3*cos(x)))*sqrt(sin(x) + 1)))

Simplificación general [src]

/ 3           \                         / 2         \
\x  + 3*cos(x)/*cos(x) - 6*(1 + sin(x))*\x  - sin(x)/
-----------------------------------------------------
                                          2          
              ____________ / 3           \           
          2*\/ 1 + sin(x) *\x  + 3*cos(x)/

\frac{- 6 \left(x^{2} - \sin{\left(x \right)}\right) \left(\sin{\left(x \right)} + 1\right) + \left(x^{3} + 3 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

((x^3 + 3*cos(x))*cos(x) - 6*(1 + sin(x))*(x^2 - sin(x)))/(2*sqrt(1 + sin(x))*(x^3 + 3*cos(x))^2)

Denominador común [src]

          2        2           2                  3             2            
     - 6*x  + 3*cos (x) + 6*sin (x) + 6*sin(x) + x *cos(x) - 6*x *sin(x)     
-----------------------------------------------------------------------------
   6   ____________        ____________    2          3   ____________       
2*x *\/ 1 + sin(x)  + 18*\/ 1 + sin(x) *cos (x) + 12*x *\/ 1 + sin(x) *cos(x)

\frac{x^{3} \cos{\left(x \right)} - 6 x^{2} \sin{\left(x \right)} - 6 x^{2} + 6 \sin^{2}{\left(x \right)} + 6 \sin{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}{2 x^{6} \sqrt{\sin{\left(x \right)} + 1} + 12 x^{3} \sqrt{\sin{\left(x \right)} + 1} \cos{\left(x \right)} + 18 \sqrt{\sin{\left(x \right)} + 1} \cos^{2}{\left(x \right)}}

(-6*x^2 + 3*cos(x)^2 + 6*sin(x)^2 + 6*sin(x) + x^3*cos(x) - 6*x^2*sin(x))/(2*x^6*sqrt(1 + sin(x)) + 18*sqrt(1 + sin(x))*cos(x)^2 + 12*x^3*sqrt(1 + sin(x))*cos(x))

Denominador racional [src]

                        2                                                                                                                              
     5   / 3           \               2             5             3    2         3                2                                    2              
- 6*x  + \x  + 3*cos(x)/ *cos(x) - 18*x *cos(x) - 6*x *sin(x) + 6*x *sin (x) + 6*x *sin(x) + 18*sin (x)*cos(x) + 18*cos(x)*sin(x) - 18*x *cos(x)*sin(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 2                                                                     
                                                     ____________ / 3           \  /   3           \                                                   
                                                   \/ 1 + sin(x) *\x  + 3*cos(x)/ *\2*x  + 6*cos(x)/

\frac{- 6 x^{5} \sin{\left(x \right)} - 6 x^{5} + 6 x^{3} \sin^{2}{\left(x \right)} + 6 x^{3} \sin{\left(x \right)} - 18 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 18 x^{2} \cos{\left(x \right)} + \left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \cos{\left(x \right)} + 18 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 18 \sin{\left(x \right)} \cos{\left(x \right)}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \left(2 x^{3} + 6 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

(-6*x^5 + (x^3 + 3*cos(x))^2*cos(x) - 18*x^2*cos(x) - 6*x^5*sin(x) + 6*x^3*sin(x)^2 + 6*x^3*sin(x) + 18*sin(x)^2*cos(x) + 18*cos(x)*sin(x) - 18*x^2*cos(x)*sin(x))/(sqrt(1 + sin(x))*(x^3 + 3*cos(x))^2*(2*x^3 + 6*cos(x)))

Respuesta numérica [src]

(1.0 + sin(x))^(-0.5)*cos(x)/(2.0*x^3 + 6.0*cos(x)) + 0.111111111111111*(1.0 + sin(x))^0.5*(3.0*sin(x) - 3.0*x^2)/(0.333333333333333*x^3 + cos(x))^2

(1.0 + sin(x))^(-0.5)*cos(x)/(2.0*x^3 + 6.0*cos(x)) + 0.111111111111111*(1.0 + sin(x))^0.5*(3.0*sin(x) - 3.0*x^2)/(0.333333333333333*x^3 + cos(x))^2

Unión de expresiones racionales [src]

/ 3           \                         /   2         \
\x  + 3*cos(x)/*cos(x) + 6*(1 + sin(x))*\- x  + sin(x)/
-------------------------------------------------------
                                           2           
               ____________ / 3           \            
           2*\/ 1 + sin(x) *\x  + 3*cos(x)/

\frac{6 \left(- x^{2} + \sin{\left(x \right)}\right) \left(\sin{\left(x \right)} + 1\right) + \left(x^{3} + 3 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

((x^3 + 3*cos(x))*cos(x) + 6*(1 + sin(x))*(-x^2 + sin(x)))/(2*sqrt(1 + sin(x))*(x^3 + 3*cos(x))^2)

Potencias [src]

     ________________________                                                                                          
    /       /   -I*x    I*x\  /             /   -I*x    I*x\\                          I*x    -I*x                     
   /      I*\- e     + e   /  |     2   3*I*\- e     + e   /|                         e      e                         
  /   1 - ------------------ *|- 3*x  - --------------------|                         ---- + -----                     
\/                2           \                  2          /                          2       2                       
------------------------------------------------------------- + -------------------------------------------------------
                                          2                          ________________________                          
                   /        I*x      -I*x\                          /       /   -I*x    I*x\                           
                   | 3   3*e      3*e    |                         /      I*\- e     + e   /  /   3      I*x      -I*x\
                   |x  + ------ + -------|                        /   1 - ------------------ *\2*x  + 3*e    + 3*e    /
                   \       2         2   /                      \/                2

\frac{\left(- 3 x^{2} - \frac{3 i \left(e^{i x} - e^{- i x}\right)}{2}\right) \sqrt{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1}}{\left(x^{3} + \frac{3 e^{i x}}{2} + \frac{3 e^{- i x}}{2}\right)^{2}} + \frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{\sqrt{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1} \left(2 x^{3} + 3 e^{i x} + 3 e^{- i x}\right)}

  ____________ /     2           \                                   
\/ 1 + sin(x) *\- 3*x  + 3*sin(x)/                cos(x)             
---------------------------------- + --------------------------------
                        2              ____________ /   3           \
         / 3           \             \/ 1 + sin(x) *\2*x  + 6*cos(x)/
         \x  + 3*cos(x)/

\frac{\left(- 3 x^{2} + 3 \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{\left(2 x^{3} + 6 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

sqrt(1 + sin(x))*(-3*x^2 + 3*sin(x))/(x^3 + 3*cos(x))^2 + cos(x)/(sqrt(1 + sin(x))*(2*x^3 + 6*cos(x)))

Abrimos la expresión [src]

                                                       2   ____________              ____________          
                    cos(x)                          3*x *\/ sin(x) + 1           3*\/ sin(x) + 1 *sin(x)   
--------------------------------------------- - ---------------------------- + ----------------------------
   3   ____________       ____________           6        2         3           6        2         3       
2*x *\/ sin(x) + 1  + 6*\/ sin(x) + 1 *cos(x)   x  + 9*cos (x) + 6*x *cos(x)   x  + 9*cos (x) + 6*x *cos(x)

- \frac{3 x^{2} \sqrt{\sin{\left(x \right)} + 1}}{x^{6} + 6 x^{3} \cos{\left(x \right)} + 9 \cos^{2}{\left(x \right)}} + \frac{3 \sqrt{\sin{\left(x \right)} + 1} \sin{\left(x \right)}}{x^{6} + 6 x^{3} \cos{\left(x \right)} + 9 \cos^{2}{\left(x \right)}} + \frac{\cos{\left(x \right)}}{2 x^{3} \sqrt{\sin{\left(x \right)} + 1} + 6 \sqrt{\sin{\left(x \right)} + 1} \cos{\left(x \right)}}

cos(x)/(2*x^3*sqrt(sin(x) + 1) + 6*sqrt(sin(x) + 1)*cos(x)) - 3*x^2*sqrt(sin(x) + 1)/(x^6 + 9*cos(x)^2 + 6*x^3*cos(x)) + 3*sqrt(sin(x) + 1)*sin(x)/(x^6 + 9*cos(x)^2 + 6*x^3*cos(x))

Compilar la expresión [src]

  ____________ /     2           \                                   
\/ 1 + sin(x) *\- 3*x  + 3*sin(x)/                cos(x)             
---------------------------------- + --------------------------------
                        2              ____________ /   3           \
         / 3           \             \/ 1 + sin(x) *\2*x  + 6*cos(x)/
         \x  + 3*cos(x)/

\frac{\left(- 3 x^{2} + 3 \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{\left(2 x^{3} + 6 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

sqrt(1 + sin(x))*(-3*x^2 + 3*sin(x))/(x^3 + 3*cos(x))^2 + cos(x)/(sqrt(1 + sin(x))*(2*x^3 + 6*cos(x)))

Combinatoria [src]

     2        2           2                  3             2       
- 6*x  + 3*cos (x) + 6*sin (x) + 6*sin(x) + x *cos(x) - 6*x *sin(x)
-------------------------------------------------------------------
                                                 2                 
                     ____________ / 3           \                  
                 2*\/ 1 + sin(x) *\x  + 3*cos(x)/

\frac{x^{3} \cos{\left(x \right)} - 6 x^{2} \sin{\left(x \right)} - 6 x^{2} + 6 \sin^{2}{\left(x \right)} + 6 \sin{\left(x \right)} + 3 \cos^{2}{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

(-6*x^2 + 3*cos(x)^2 + 6*sin(x)^2 + 6*sin(x) + x^3*cos(x) - 6*x^2*sin(x))/(2*sqrt(1 + sin(x))*(x^3 + 3*cos(x))^2)

Parte trigonométrica [src]

      _________________                                                                        
     /          1       /     2        3     \                                                 
    /  1 + ----------- *|- 3*x  + -----------|                                                 
   /          /    pi\  |            /    pi\|                                                 
  /        sec|x - --|  |         sec|x - --||                                                 
\/            \    2 /  \            \    2 //                         1                       
---------------------------------------------- + ----------------------------------------------
                             2                         _________________                       
                / 3     3   \                         /          1       /   3     6   \       
                |x  + ------|                        /  1 + ----------- *|2*x  + ------|*sec(x)
                \     sec(x)/                       /          /    pi\  \       sec(x)/       
                                                   /        sec|x - --|                        
                                                 \/            \    2 /

\frac{\sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \left(- 3 x^{2} + \frac{3}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)}{\left(x^{3} + \frac{3}{\sec{\left(x \right)}}\right)^{2}} + \frac{1}{\sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \left(2 x^{3} + \frac{6}{\sec{\left(x \right)}}\right) \sec{\left(x \right)}}

    ____________                                                                      
   /       1     /     2     3   \                                                    
  /  1 + ------ *|- 3*x  + ------|                                                    
\/       csc(x)  \         csc(x)/                           1                        
---------------------------------- + -------------------------------------------------
                         2               ____________                                 
       / 3        3     \               /       1     /   3        6     \    /pi    \
       |x  + -----------|              /  1 + ------ *|2*x  + -----------|*csc|-- - x|
       |        /pi    \|            \/       csc(x)  |          /pi    \|    \2     /
       |     csc|-- - x||                             |       csc|-- - x||            
       \        \2     //                             \          \2     //

\frac{\sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(- 3 x^{2} + \frac{3}{\csc{\left(x \right)}}\right)}{\left(x^{3} + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{2}} + \frac{1}{\sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(2 x^{3} + \frac{6}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}

                           /pi      \    3    /    pi\              
                      3*sin|-- + 2*x|   x *sin|x + --|              
9      2                   \2       /         \    2 /      2       
- - 3*x  + 3*sin(x) - --------------- + -------------- - 3*x *sin(x)
4                            4                2                     
--------------------------------------------------------------------
                                                   2                
                  ____________ / 3        /    pi\\                 
                \/ 1 + sin(x) *|x  + 3*sin|x + --||                 
                               \          \    2 //

\frac{\frac{x^{3} \sin{\left(x + \frac{\pi}{2} \right)}}{2} - 3 x^{2} \sin{\left(x \right)} - 3 x^{2} + 3 \sin{\left(x \right)} - \frac{3 \sin{\left(2 x + \frac{\pi}{2} \right)}}{4} + \frac{9}{4}}{\left(x^{3} + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

                                             3            2 
9      2     3             3                x          3*x  
- - 3*x  + ------ - --------------- + ------------- - ------
4          csc(x)        /pi      \        /pi    \   csc(x)
                    4*csc|-- - 2*x|   2*csc|-- - x|         
                         \2       /        \2     /         
------------------------------------------------------------
                ____________                   2            
               /       1     / 3        3     \             
              /  1 + ------ *|x  + -----------|             
            \/       csc(x)  |        /pi    \|             
                             |     csc|-- - x||             
                             \        \2     //

\frac{\frac{x^{3}}{2 \csc{\left(- x + \frac{\pi}{2} \right)}} - 3 x^{2} - \frac{3 x^{2}}{\csc{\left(x \right)}} + \frac{9}{4} - \frac{3}{4 \csc{\left(- 2 x + \frac{\pi}{2} \right)}} + \frac{3}{\csc{\left(x \right)}}}{\sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(x^{3} + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{2}}

                                    3                     
9      2              3*cos(2*x)   x *cos(x)      2       
- - 3*x  + 3*sin(x) - ---------- + --------- - 3*x *sin(x)
4                         4            2                  
----------------------------------------------------------
                                           2              
               ____________ / 3           \               
             \/ 1 + sin(x) *\x  + 3*cos(x)/

\frac{\frac{x^{3} \cos{\left(x \right)}}{2} - 3 x^{2} \sin{\left(x \right)} - 3 x^{2} + 3 \sin{\left(x \right)} - \frac{3 \cos{\left(2 x \right)}}{4} + \frac{9}{4}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

        _________________                                                                                          
       /            /x\   /                /x\ \                                                                   
      /        2*tan|-|   |           6*tan|-| |                                                                   
     /              \2/   |     2          \2/ |                                                                   
    /    1 + ----------- *|- 3*x  + -----------|                                                                   
   /                2/x\  |                2/x\|                                    2/x\                           
  /          1 + tan |-|  |         1 + tan |-||                             1 - tan |-|                           
\/                   \2/  \                 \2//                                     \2/                           
------------------------------------------------ + ----------------------------------------------------------------
                                  2                                      _________________                         
            /       /       2/x\\\                                      /            /x\   /         /       2/x\\\
            |     3*|1 - tan |-|||                                     /        2*tan|-|   |       6*|1 - tan |-|||
            | 3     \        \2//|                 /       2/x\\      /              \2/   |   3     \        \2//|
            |x  + ---------------|                 |1 + tan |-||*    /    1 + ----------- *|2*x  + ---------------|
            |              2/x\  |                 \        \2//    /                2/x\  |                2/x\  |
            |       1 + tan |-|  |                                 /          1 + tan |-|  |         1 + tan |-|  |
            \               \2/  /                               \/                   \2/  \                 \2/  /

\frac{\sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- 3 x^{2} + \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(x^{3} + \frac{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(2 x^{3} + \frac{6 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}

                                                _________________                     
                                               /        /    pi\  /   2      /    pi\\
                                          3*  /  1 + cos|x - --| *|- x  + cos|x - --||
                 cos(x)                     \/          \    2 /  \          \    2 //
--------------------------------------- + --------------------------------------------
      _________________                                                2              
     /        /    pi\  / 3           \                 / 3           \               
2*  /  1 + cos|x - --| *\x  + 3*cos(x)/                 \x  + 3*cos(x)/               
  \/          \    2 /

\frac{3 \left(- x^{2} + \cos{\left(x - \frac{\pi}{2} \right)}\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}

                  /x\                        3 /        2/x\\      2    /x\
             6*cot|-|      /        2   \   x *|-1 + cot |-||   6*x *cot|-|
9      2          \2/    3*\-1 + cot (x)/      \         \2//           \2/
- - 3*x  + ----------- - ---------------- + ----------------- - -----------
4                 2/x\     /       2   \       /       2/x\\           2/x\
           1 + cot |-|   4*\1 + cot (x)/     2*|1 + cot |-||    1 + cot |-|
                   \2/                         \        \2//            \2/
---------------------------------------------------------------------------
                     _________________                        2            
                    /            /x\   /       /        2/x\\\             
                   /        2*cot|-|   |     3*|-1 + cot |-|||             
                  /              \2/   | 3     \         \2//|             
                 /    1 + ----------- *|x  + ----------------|             
                /                2/x\  |              2/x\   |             
               /          1 + cot |-|  |       1 + cot |-|   |             
             \/                   \2/  \               \2/   /

\frac{\frac{x^{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} - 3 x^{2} - \frac{6 x^{2} \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{3 \left(\cot^{2}{\left(x \right)} - 1\right)}{4 \left(\cot^{2}{\left(x \right)} + 1\right)} + \frac{9}{4} + \frac{6 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}{\sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(x^{3} + \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}}

          _________________                                                                                         
         /            /x\   /              /x\ \                                                                    
        /        2*cot|-|   |         2*cot|-| |                                                                    
       /              \2/   |   2          \2/ |                                                                    
3*    /    1 + ----------- *|- x  + -----------|                                                                    
     /                2/x\  |              2/x\|                                      2/x\                          
    /          1 + cot |-|  |       1 + cot |-||                              -1 + cot |-|                          
  \/                   \2/  \               \2//                                       \2/                          
------------------------------------------------ + -----------------------------------------------------------------
                                   2                                       _________________                        
            /       /        2/x\\\                                       /            /x\   /       /        2/x\\\
            |     3*|-1 + cot |-|||                                      /        2*cot|-|   |     3*|-1 + cot |-|||
            | 3     \         \2//|                  /       2/x\\      /              \2/   | 3     \         \2//|
            |x  + ----------------|                2*|1 + cot |-||*    /    1 + ----------- *|x  + ----------------|
            |              2/x\   |                  \        \2//    /                2/x\  |              2/x\   |
            |       1 + cot |-|   |                                  /          1 + cot |-|  |       1 + cot |-|   |
            \               \2/   /                                \/                   \2/  \               \2/   /

\frac{3 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- x^{2} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(x^{3} + \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{2 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(x^{3} + \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}

  ____________ /     2           \                                   
\/ 1 + sin(x) *\- 3*x  + 3*sin(x)/                cos(x)             
---------------------------------- + --------------------------------
                        2              ____________ /   3           \
         / 3           \             \/ 1 + sin(x) *\2*x  + 6*cos(x)/
         \x  + 3*cos(x)/

\frac{\left(- 3 x^{2} + 3 \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{\left(2 x^{3} + 6 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

                                                     /    pi\             
  ____________ /     2           \                sin|x + --|             
\/ 1 + sin(x) *\- 3*x  + 3*sin(x)/                   \    2 /             
---------------------------------- + -------------------------------------
                          2            ____________ /   3        /    pi\\
      / 3        /    pi\\           \/ 1 + sin(x) *|2*x  + 6*sin|x + --||
      |x  + 3*sin|x + --||                          \            \    2 //
      \          \    2 //

\frac{\left(- 3 x^{2} + 3 \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)^{2}} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\left(2 x^{3} + 6 \sin{\left(x + \frac{\pi}{2} \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

                                       ____________ /   2         \
             cos(x)                3*\/ sin(x) + 1 *\- x  + sin(x)/
-------------------------------- + --------------------------------
    ____________ / 3           \                          2        
2*\/ 1 + sin(x) *\x  + 3*cos(x)/           / 3           \         
                                           \x  + 3*cos(x)/

\frac{3 \left(- x^{2} + \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

                                          3             2   
9      2        3            3           x           3*x    
- - 3*x  + ----------- - ---------- + -------- - -----------
4             /    pi\   4*sec(2*x)   2*sec(x)      /    pi\
           sec|x - --|                           sec|x - --|
              \    2 /                              \    2 /
------------------------------------------------------------
                 _________________              2           
                /          1       / 3     3   \            
               /  1 + ----------- *|x  + ------|            
              /          /    pi\  \     sec(x)/            
             /        sec|x - --|                           
           \/            \    2 /

\frac{\frac{x^{3}}{2 \sec{\left(x \right)}} - 3 x^{2} - \frac{3 x^{2}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{9}{4} + \frac{3}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{3}{4 \sec{\left(2 x \right)}}}{\sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \left(x^{3} + \frac{3}{\sec{\left(x \right)}}\right)^{2}}

                  /x\                       3 /       2/x\\      2    /x\
             6*tan|-|      /       2   \   x *|1 - tan |-||   6*x *tan|-|
9      2          \2/    3*\1 - tan (x)/      \        \2//           \2/
- - 3*x  + ----------- - --------------- + ---------------- - -----------
4                 2/x\     /       2   \     /       2/x\\           2/x\
           1 + tan |-|   4*\1 + tan (x)/   2*|1 + tan |-||    1 + tan |-|
                   \2/                       \        \2//            \2/
-------------------------------------------------------------------------
                    _________________                       2            
                   /            /x\   /       /       2/x\\\             
                  /        2*tan|-|   |     3*|1 - tan |-|||             
                 /              \2/   | 3     \        \2//|             
                /    1 + ----------- *|x  + ---------------|             
               /                2/x\  |              2/x\  |             
              /          1 + tan |-|  |       1 + tan |-|  |             
            \/                   \2/  \               \2/  /

\frac{\frac{x^{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} - 3 x^{2} - \frac{6 x^{2} \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{3 \left(1 - \tan^{2}{\left(x \right)}\right)}{4 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{9}{4} + \frac{6 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}{\sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(x^{3} + \frac{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}}

                                         3                          
9      2        /    pi\   3*cos(2*x)   x *cos(x)      2    /    pi\
- - 3*x  + 3*cos|x - --| - ---------- + --------- - 3*x *cos|x - --|
4               \    2 /       4            2               \    2 /
--------------------------------------------------------------------
                   _________________                2               
                  /        /    pi\  / 3           \                
                 /  1 + cos|x - --| *\x  + 3*cos(x)/                
               \/          \    2 /

\frac{\frac{x^{3} \cos{\left(x \right)}}{2} - 3 x^{2} \cos{\left(x - \frac{\pi}{2} \right)} - 3 x^{2} - \frac{3 \cos{\left(2 x \right)}}{4} + 3 \cos{\left(x - \frac{\pi}{2} \right)} + \frac{9}{4}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}

    ____________                                                            
   /       1     /     2     3   \                                          
  /  1 + ------ *|- 3*x  + ------|                                          
\/       csc(x)  \         csc(x)/                      1                   
---------------------------------- + ---------------------------------------
                       2                 ____________                       
          / 3     3   \                 /       1     /   3     6   \       
          |x  + ------|                /  1 + ------ *|2*x  + ------|*sec(x)
          \     sec(x)/              \/       csc(x)  \       sec(x)/

\frac{\sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(- 3 x^{2} + \frac{3}{\csc{\left(x \right)}}\right)}{\left(x^{3} + \frac{3}{\sec{\left(x \right)}}\right)^{2}} + \frac{1}{\sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(2 x^{3} + \frac{6}{\sec{\left(x \right)}}\right) \sec{\left(x \right)}}

                                                          ____________              
                                                         /       1     /  1       2\
                                                    3*  /  1 + ------ *|------ - x |
                        1                             \/       csc(x)  \csc(x)     /
------------------------------------------------- + --------------------------------
      ____________                                                          2       
     /       1     / 3        3     \    /pi    \         / 3        3     \        
2*  /  1 + ------ *|x  + -----------|*csc|-- - x|         |x  + -----------|        
  \/       csc(x)  |        /pi    \|    \2     /         |        /pi    \|        
                   |     csc|-- - x||                     |     csc|-- - x||        
                   \        \2     //                     \        \2     //

\frac{3 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(- x^{2} + \frac{1}{\csc{\left(x \right)}}\right)}{\left(x^{3} + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{2}} + \frac{1}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \left(x^{3} + \frac{3}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}

    _________________                                                                   
   /        /    pi\  /     2        /    pi\\                                          
  /  1 + cos|x - --| *|- 3*x  + 3*cos|x - --||                                          
\/          \    2 /  \              \    2 //                    cos(x)                
---------------------------------------------- + ---------------------------------------
                              2                      _________________                  
               / 3           \                      /        /    pi\  /   3           \
               \x  + 3*cos(x)/                     /  1 + cos|x - --| *\2*x  + 6*cos(x)/
                                                 \/          \    2 /

\frac{\left(- 3 x^{2} + 3 \cos{\left(x - \frac{\pi}{2} \right)}\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{\left(2 x^{3} + 6 \cos{\left(x \right)}\right) \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}

                           2       3                     
       2              3*cos (x)   x *cos(x)      2       
3 - 3*x  + 3*sin(x) - --------- + --------- - 3*x *sin(x)
                          2           2                  
---------------------------------------------------------
                                           2             
               ____________ / 3           \              
             \/ 1 + sin(x) *\x  + 3*cos(x)/

\frac{\frac{x^{3} \cos{\left(x \right)}}{2} - 3 x^{2} \sin{\left(x \right)} - 3 x^{2} + 3 \sin{\left(x \right)} - \frac{3 \cos^{2}{\left(x \right)}}{2} + 3}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2} \sqrt{\sin{\left(x \right)} + 1}}

        _________________                                                                                           
       /            /x\   /                /x\ \                                                                    
      /        2*cot|-|   |           6*cot|-| |                                                                    
     /              \2/   |     2          \2/ |                                                                    
    /    1 + ----------- *|- 3*x  + -----------|                                                                    
   /                2/x\  |                2/x\|                                      2/x\                          
  /          1 + cot |-|  |         1 + cot |-||                              -1 + cot |-|                          
\/                   \2/  \                 \2//                                       \2/                          
------------------------------------------------ + -----------------------------------------------------------------
                                   2                                     _________________                          
            /       /        2/x\\\                                     /            /x\   /         /        2/x\\\
            |     3*|-1 + cot |-|||                                    /        2*cot|-|   |       6*|-1 + cot |-|||
            | 3     \         \2//|                /       2/x\\      /              \2/   |   3     \         \2//|
            |x  + ----------------|                |1 + cot |-||*    /    1 + ----------- *|2*x  + ----------------|
            |              2/x\   |                \        \2//    /                2/x\  |                2/x\   |
            |       1 + cot |-|   |                                /          1 + cot |-|  |         1 + cot |-|   |
            \               \2/   /                              \/                   \2/  \                 \2/   /

\frac{\sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- 3 x^{2} + \frac{6 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(x^{3} + \frac{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(2 x^{3} + \frac{6 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}

          _________________                                                                                        
         /            /x\   /              /x\ \                                                                   
        /        2*tan|-|   |         2*tan|-| |                                                                   
       /              \2/   |   2          \2/ |                                                                   
3*    /    1 + ----------- *|- x  + -----------|                                                                   
     /                2/x\  |              2/x\|                                    2/x\                           
    /          1 + tan |-|  |       1 + tan |-||                             1 - tan |-|                           
  \/                   \2/  \               \2//                                     \2/                           
------------------------------------------------ + ----------------------------------------------------------------
                                  2                                        _________________                       
            /       /       2/x\\\                                        /            /x\   /       /       2/x\\\
            |     3*|1 - tan |-|||                                       /        2*tan|-|   |     3*|1 - tan |-|||
            | 3     \        \2//|                   /       2/x\\      /              \2/   | 3     \        \2//|
            |x  + ---------------|                 2*|1 + tan |-||*    /    1 + ----------- *|x  + ---------------|
            |              2/x\  |                   \        \2//    /                2/x\  |              2/x\  |
            |       1 + tan |-|  |                                   /          1 + tan |-|  |       1 + tan |-|  |
            \               \2/  /                                 \/                   \2/  \               \2/  /

\frac{3 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(- x^{2} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)}{\left(x^{3} + \frac{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{2}} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(x^{3} + \frac{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}

                                       ____________ /   2         \
             cos(x)                3*\/ 1 + sin(x) *\- x  + sin(x)/
-------------------------------- + --------------------------------
    ____________ / 3           \                          2        
2*\/ 1 + sin(x) *\x  + 3*cos(x)/           / 3           \         
                                           \x  + 3*cos(x)/

\frac{3 \left(- x^{2} + \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \cos{\left(x \right)}\right)^{2}} + \frac{\cos{\left(x \right)}}{2 \left(x^{3} + 3 \cos{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

                /    pi\                                                
             sin|x + --|                    ____________ /   2         \
                \    2 /                3*\/ 1 + sin(x) *\- x  + sin(x)/
------------------------------------- + --------------------------------
    ____________ / 3        /    pi\\                            2      
2*\/ 1 + sin(x) *|x  + 3*sin|x + --||        / 3        /    pi\\       
                 \          \    2 //        |x  + 3*sin|x + --||       
                                             \          \    2 //

\frac{3 \left(- x^{2} + \sin{\left(x \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}{\left(x^{3} + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right)^{2}} + \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{2 \left(x^{3} + 3 \sin{\left(x + \frac{\pi}{2} \right)}\right) \sqrt{\sin{\left(x \right)} + 1}}

                                                         _________________                   
                                                        /          1       /     1         2\
                                                 3*    /  1 + ----------- *|----------- - x |
                                                      /          /    pi\  |   /    pi\     |
                                                     /        sec|x - --|  |sec|x - --|     |
                      1                            \/            \    2 /  \   \    2 /     /
---------------------------------------------- + --------------------------------------------
        _________________                                                    2               
       /          1       / 3     3   \                         / 3     3   \                
2*    /  1 + ----------- *|x  + ------|*sec(x)                  |x  + ------|                
     /          /    pi\  \     sec(x)/                         \     sec(x)/                
    /        sec|x - --|                                                                     
  \/            \    2 /

\frac{3 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \left(- x^{2} + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)}{\left(x^{3} + \frac{3}{\sec{\left(x \right)}}\right)^{2}} + \frac{1}{2 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \left(x^{3} + \frac{3}{\sec{\left(x \right)}}\right) \sec{\left(x \right)}}

1/(2*sqrt(1 + 1/sec(x - pi/2))*(x^3 + 3/sec(x))*sec(x)) + 3*sqrt(1 + 1/sec(x - pi/2))*(1/sec(x - pi/2) - x^2)/(x^3 + 3/sec(x))^2

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¿Cómo vas a descomponer esta sqrt(sin(x)+1)(-3x^2+3sin(x))/(x^3+3cos(x))^2+cos(x)/(2(x^3+3cos(x))*sqrt(sin(x)+1)) expresión en fracciones?