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Simplificación de expresiones/ Descomposición en fracciones simples/ log(((4*sin(x))/(1+cos(x))-sqrt(41)+5)/(5+sqrt(41)+(4*sin(x))/(1+cos(x))))/sqrt(41)

¿Cómo vas a descomponer esta log(((4*sin(x))/(1+cos(x))-sqrt(41)+5)/(5+sqrt(41)+(4*sin(x))/(1+cos(x))))/sqrt(41) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   / 4*sin(x)      ____    \
   |---------- - \/ 41  + 5|
   |1 + cos(x)             |
log|-----------------------|
   |      ____    4*sin(x) |
   |5 + \/ 41  + ----------|
   \             1 + cos(x)/
----------------------------
             ____           
           \/ 41
log⁡((−41+4sin⁡(x)cos⁡(x)+1)+5(5+41)+4sin⁡(x)cos⁡(x)+1)41\frac{\log{\left(\frac{\left(- \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) + 5}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{\sqrt{41}} 
log(((4*sin(x))/(1 + cos(x)) - sqrt(41) + 5)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))))/sqrt(41)
Descomposición de una fracción [src] 
sqrt(41)*log(5/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))) - sqrt(41)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))) + 4*sin(x)/(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + (4*sin(x))/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x))))/41
41log⁡(4sin⁡(x)5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1−41(5+41)+4sin⁡(x)cos⁡(x)+1+5(5+41)+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{4 \sin{\left(x \right)}}{5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{\sqrt{41}}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} + \frac{5}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
          /                                     ____                                                                               \
  ____    |           5                       \/ 41                                          4*sin(x)                              |
\/ 41 *log|----------------------- - ----------------------- + --------------------------------------------------------------------|
          |      ____    4*sin(x)          ____    4*sin(x)          ____                ____           4*sin(x)    4*cos(x)*sin(x)|
          |5 + \/ 41  + ----------   5 + \/ 41  + ----------   5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------|
          \             1 + cos(x)                1 + cos(x)                                           1 + cos(x)      1 + cos(x)  /
------------------------------------------------------------------------------------------------------------------------------------
                                                                 41
Simplificación general [src] 
          /                        /      ____\\
  ____    |4*sin(x) + (1 + cos(x))*\5 - \/ 41 /|
\/ 41 *log|------------------------------------|
          |                        /      ____\|
          \4*sin(x) + (1 + cos(x))*\5 + \/ 41 //
------------------------------------------------
                       41
41log⁡((5−41)(cos⁡(x)+1)+4sin⁡(x)(5+41)(cos⁡(x)+1)+4sin⁡(x))41\frac{\sqrt{41} \log{\left(\frac{\left(5 - \sqrt{41}\right) \left(\cos{\left(x \right)} + 1\right) + 4 \sin{\left(x \right)}}{\left(5 + \sqrt{41}\right) \left(\cos{\left(x \right)} + 1\right) + 4 \sin{\left(x \right)}} \right)}}{41} 
sqrt(41)*log((4*sin(x) + (1 + cos(x))*(5 - sqrt(41)))/(4*sin(x) + (1 + cos(x))*(5 + sqrt(41))))/41
Respuesta numérica [src] 
0.156173761888606*log(((4*sin(x))/(1 + cos(x)) - sqrt(41) + 5)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))))
0.156173761888606*log(((4*sin(x))/(1 + cos(x)) - sqrt(41) + 5)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))))
Potencias [src] 
          /      ____    4*sin(x) \
          |5 - \/ 41  + ----------|
  ____    |             1 + cos(x)|
\/ 41 *log|-----------------------|
          |      ____    4*sin(x) |
          |5 + \/ 41  + ----------|
          \             1 + cos(x)/
-----------------------------------
                 41
41log⁡(−41+5+4sin⁡(x)cos⁡(x)+15+41+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
          /                 /   -I*x    I*x\\
          |      ____   2*I*\- e     + e   /|
          |5 - \/ 41  - --------------------|
          |                    I*x    -I*x  |
          |                   e      e      |
          |               1 + ---- + -----  |
  ____    |                    2       2    |
\/ 41 *log|---------------------------------|
          |                 /   -I*x    I*x\|
          |      ____   2*I*\- e     + e   /|
          |5 + \/ 41  - --------------------|
          |                    I*x    -I*x  |
          |                   e      e      |
          |               1 + ---- + -----  |
          \                    2       2    /
---------------------------------------------
                      41
41log⁡(−2i(eix−e−ix)eix2+1+e−ix2−41+5−2i(eix−e−ix)eix2+1+e−ix2+5+41)41\frac{\sqrt{41} \log{\left(\frac{- \frac{2 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} - \sqrt{41} + 5}{- \frac{2 i \left(e^{i x} - e^{- i x}\right)}{\frac{e^{i x}}{2} + 1 + \frac{e^{- i x}}{2}} + 5 + \sqrt{41}} \right)}}{41} 
sqrt(41)*log((5 - sqrt(41) - 2*i*(-exp(-i*x) + exp(i*x))/(1 + exp(i*x)/2 + exp(-i*x)/2))/(5 + sqrt(41) - 2*i*(-exp(-i*x) + exp(i*x))/(1 + exp(i*x)/2 + exp(-i*x)/2)))/41
Denominador común [src] 
          /                                     ____                                                                               \
  ____    |           5                       \/ 41                                          4*sin(x)                              |
\/ 41 *log|----------------------- - ----------------------- + --------------------------------------------------------------------|
          |      ____    4*sin(x)          ____    4*sin(x)          ____                ____           4*sin(x)    4*cos(x)*sin(x)|
          |5 + \/ 41  + ----------   5 + \/ 41  + ----------   5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------|
          \             1 + cos(x)                1 + cos(x)                                           1 + cos(x)      1 + cos(x)  /
------------------------------------------------------------------------------------------------------------------------------------
                                                                 41
41log⁡(4sin⁡(x)5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1−415+41+4sin⁡(x)cos⁡(x)+1+55+41+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{4 \sin{\left(x \right)}}{5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{\sqrt{41}}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} + \frac{5}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
sqrt(41)*log(5/(5 + sqrt(41) + 4*sin(x)/(1 + cos(x))) - sqrt(41)/(5 + sqrt(41) + 4*sin(x)/(1 + cos(x))) + 4*sin(x)/(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + 4*sin(x)/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x))))/41
Denominador racional [src] 
          /         ____                 ____ /      ____                ____           4*sin(x)    4*cos(x)*sin(x)\     /      ____    4*sin(x) \              ____          5*4*sin(x)   20*cos(x)*sin(x)\
          |25 + 5*\/ 41  + 25*cos(x) - \/ 41 *|5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------| + 4*|5 + \/ 41  + ----------|*sin(x) + 5*\/ 41 *cos(x) + ---------- + ----------------|
  ____    |                                   \                                        1 + cos(x)      1 + cos(x)  /     \             1 + cos(x)/                            1 + cos(x)      1 + cos(x)   |
\/ 41 *log|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
          |                                                /      ____    4*sin(x) \ /      ____                ____           4*sin(x)    4*cos(x)*sin(x)\                                                |
          |                                                |5 + \/ 41  + ----------|*|5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------|                                                |
          \                                                \             1 + cos(x)/ \                                        1 + cos(x)      1 + cos(x)  /                                                /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                     41
41log⁡(4((5+41)+4sin⁡(x)cos⁡(x)+1)sin⁡(x)−41(5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1)+25cos⁡(x)+541cos⁡(x)+25+541+20sin⁡(x)cos⁡(x)cos⁡(x)+1+5⋅4sin⁡(x)cos⁡(x)+1((5+41)+4sin⁡(x)cos⁡(x)+1)(5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1))41\frac{\sqrt{41} \log{\left(\frac{4 \left(\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) \sin{\left(x \right)} - \sqrt{41} \left(5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) + 25 \cos{\left(x \right)} + 5 \sqrt{41} \cos{\left(x \right)} + 25 + 5 \sqrt{41} + \frac{20 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{5 \cdot 4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{\left(\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) \left(5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)} \right)}}{41} 
sqrt(41)*log((25 + 5*sqrt(41) + 25*cos(x) - sqrt(41)*(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + (4*sin(x))/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x))) + 4*(5 + sqrt(41) + (4*sin(x))/(1 + cos(x)))*sin(x) + 5*sqrt(41)*cos(x) + 5*(4*sin(x))/(1 + cos(x)) + 20*cos(x)*sin(x)/(1 + cos(x)))/((5 + sqrt(41) + (4*sin(x))/(1 + cos(x)))*(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + (4*sin(x))/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x)))))/41
Combinatoria [src] 
          /                                     ____                                                                               \
  ____    |           5                       \/ 41                                          4*sin(x)                              |
\/ 41 *log|----------------------- - ----------------------- + --------------------------------------------------------------------|
          |      ____    4*sin(x)          ____    4*sin(x)          ____                ____           4*sin(x)    4*cos(x)*sin(x)|
          |5 + \/ 41  + ----------   5 + \/ 41  + ----------   5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------|
          \             1 + cos(x)                1 + cos(x)                                           1 + cos(x)      1 + cos(x)  /
------------------------------------------------------------------------------------------------------------------------------------
                                                                 41
41log⁡(4sin⁡(x)5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1−415+41+4sin⁡(x)cos⁡(x)+1+55+41+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{4 \sin{\left(x \right)}}{5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{\sqrt{41}}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} + \frac{5}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
sqrt(41)*log(5/(5 + sqrt(41) + 4*sin(x)/(1 + cos(x))) - sqrt(41)/(5 + sqrt(41) + 4*sin(x)/(1 + cos(x))) + 4*sin(x)/(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + 4*sin(x)/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x))))/41
Abrimos la expresión [src] 
          /                                     ____                                                                               \
  ____    |           5                       \/ 41                                          4*sin(x)                              |
\/ 41 *log|----------------------- - ----------------------- + --------------------------------------------------------------------|
          |      ____    4*sin(x)          ____    4*sin(x)          ____                ____           4*sin(x)    4*cos(x)*sin(x)|
          |5 + \/ 41  + ----------   5 + \/ 41  + ----------   5 + \/ 41  + 5*cos(x) + \/ 41 *cos(x) + ---------- + ---------------|
          \             1 + cos(x)                1 + cos(x)                                           1 + cos(x)      1 + cos(x)  /
------------------------------------------------------------------------------------------------------------------------------------
                                                                 41
41log⁡(4sin⁡(x)5cos⁡(x)+41cos⁡(x)+5+41+4sin⁡(x)cos⁡(x)cos⁡(x)+1+4sin⁡(x)cos⁡(x)+1−41(5+41)+4sin⁡(x)cos⁡(x)+1+5(5+41)+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{4 \sin{\left(x \right)}}{5 \cos{\left(x \right)} + \sqrt{41} \cos{\left(x \right)} + 5 + \sqrt{41} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} + 1} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} - \frac{\sqrt{41}}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} + \frac{5}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
sqrt(41)*log(5/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))) - sqrt(41)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))) + 4*sin(x)/(5 + sqrt(41) + 5*cos(x) + sqrt(41)*cos(x) + (4*sin(x))/(1 + cos(x)) + 4*cos(x)*sin(x)/(1 + cos(x))))/41
Compilar la expresión [src] 
          / 4*sin(x)      ____    \
          |---------- - \/ 41  + 5|
  ____    |1 + cos(x)             |
\/ 41 *log|-----------------------|
          |      ____    4*sin(x) |
          |5 + \/ 41  + ----------|
          \             1 + cos(x)/
-----------------------------------
                 41
41log⁡((−41+4sin⁡(x)cos⁡(x)+1)+5(5+41)+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{\left(- \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right) + 5}{\left(5 + \sqrt{41}\right) + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
sqrt(41)*log(((4*sin(x))/(1 + cos(x)) - sqrt(41) + 5)/(5 + sqrt(41) + (4*sin(x))/(1 + cos(x))))/41
Parte trigonométrica [src] 
          /      ____    4*sin(x) \
          |5 - \/ 41  + ----------|
  ____    |             1 + cos(x)|
\/ 41 *log|-----------------------|
          |      ____    4*sin(x) |
          |5 + \/ 41  + ----------|
          \             1 + cos(x)/
-----------------------------------
                 41
41log⁡(−41+5+4sin⁡(x)cos⁡(x)+15+41+4sin⁡(x)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
          /      ____              4            \
          |5 - \/ 41  + ------------------------|
          |             /         1     \       |
          |             |1 + -----------|*csc(x)|
          |             |       /pi    \|       |
          |             |    csc|-- - x||       |
  ____    |             \       \2     //       |
\/ 41 *log|-------------------------------------|
          |      ____              4            |
          |5 + \/ 41  + ------------------------|
          |             /         1     \       |
          |             |1 + -----------|*csc(x)|
          |             |       /pi    \|       |
          |             |    csc|-- - x||       |
          \             \       \2     //       /
-------------------------------------------------
                        41
41log⁡(−41+5+4(1+1csc⁡(−x+π2))csc⁡(x)5+41+4(1+1csc⁡(−x+π2))csc⁡(x))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}}{5 + \sqrt{41} + \frac{4}{\left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}} \right)}}{41} 
          /      ____       4*sin(x)   \
          |5 - \/ 41  + ---------------|
          |                    /    pi\|
          |             1 + sin|x + --||
  ____    |                    \    2 /|
\/ 41 *log|----------------------------|
          |      ____       4*sin(x)   |
          |5 + \/ 41  + ---------------|
          |                    /    pi\|
          |             1 + sin|x + --||
          \                    \    2 //
----------------------------------------
                   41
41log⁡(−41+5+4sin⁡(x)sin⁡(x+π2)+15+41+4sin⁡(x)sin⁡(x+π2)+1)41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}}{5 + \sqrt{41} + \frac{4 \sin{\left(x \right)}}{\sin{\left(x + \frac{\pi}{2} \right)} + 1}} \right)}}{41} 
          /                              /x\            \
          |                         8*cot|-|            |
          |      ____                    \2/            |
          |5 - \/ 41  + --------------------------------|
          |                           /            2/x\\|
          |                           |    -1 + cot |-|||
          |             /       2/x\\ |             \2/||
          |             |1 + cot |-||*|1 + ------------||
          |             \        \2// |           2/x\ ||
          |                           |    1 + cot |-| ||
  ____    |                           \            \2/ /|
\/ 41 *log|---------------------------------------------|
          |                              /x\            |
          |                         8*cot|-|            |
          |      ____                    \2/            |
          |5 + \/ 41  + --------------------------------|
          |                           /            2/x\\|
          |                           |    -1 + cot |-|||
          |             /       2/x\\ |             \2/||
          |             |1 + cot |-||*|1 + ------------||
          |             \        \2// |           2/x\ ||
          |                           |    1 + cot |-| ||
          \                           \            \2/ //
---------------------------------------------------------
                            41
41log⁡(−41+5+8cot⁡(x2)(cot⁡2(x2)−1cot⁡2(x2)+1+1)(cot⁡2(x2)+1)5+41+8cot⁡(x2)(cot⁡2(x2)−1cot⁡2(x2)+1+1)(cot⁡2(x2)+1))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{8 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{5 + \sqrt{41} + \frac{8 \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}} \right)}}{41} 
          /      ____            4         \
          |5 - \/ 41  + -------------------|
          |             /      1   \       |
          |             |1 + ------|*csc(x)|
  ____    |             \    sec(x)/       |
\/ 41 *log|--------------------------------|
          |      ____            4         |
          |5 + \/ 41  + -------------------|
          |             /      1   \       |
          |             |1 + ------|*csc(x)|
          \             \    sec(x)/       /
--------------------------------------------
                     41
41log⁡(−41+5+4(1+1sec⁡(x))csc⁡(x)5+41+4(1+1sec⁡(x))csc⁡(x))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}}{5 + \sqrt{41} + \frac{4}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \csc{\left(x \right)}}} \right)}}{41} 
          /                  /    pi\\
          |             4*cos|x - --||
          |      ____        \    2 /|
          |5 - \/ 41  + -------------|
  ____    |               1 + cos(x) |
\/ 41 *log|--------------------------|
          |                  /    pi\|
          |             4*cos|x - --||
          |      ____        \    2 /|
          |5 + \/ 41  + -------------|
          \               1 + cos(x) /
--------------------------------------
                  41
41log⁡(−41+5+4cos⁡(x−π2)cos⁡(x)+15+41+4cos⁡(x−π2)cos⁡(x)+1)41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}}{5 + \sqrt{41} + \frac{4 \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} + 1}} \right)}}{41} 
          /                              /x\           \
          |                         8*tan|-|           |
          |      ____                    \2/           |
          |5 - \/ 41  + -------------------------------|
          |                           /           2/x\\|
          |                           |    1 - tan |-|||
          |             /       2/x\\ |            \2/||
          |             |1 + tan |-||*|1 + -----------||
          |             \        \2// |           2/x\||
          |                           |    1 + tan |-|||
  ____    |                           \            \2//|
\/ 41 *log|--------------------------------------------|
          |                              /x\           |
          |                         8*tan|-|           |
          |      ____                    \2/           |
          |5 + \/ 41  + -------------------------------|
          |                           /           2/x\\|
          |                           |    1 - tan |-|||
          |             /       2/x\\ |            \2/||
          |             |1 + tan |-||*|1 + -----------||
          |             \        \2// |           2/x\||
          |                           |    1 + tan |-|||
          \                           \            \2///
--------------------------------------------------------
                           41
41log⁡(−41+5+8tan⁡(x2)(1−tan⁡2(x2)tan⁡2(x2)+1+1)(tan⁡2(x2)+1)5+41+8tan⁡(x2)(1−tan⁡2(x2)tan⁡2(x2)+1+1)(tan⁡2(x2)+1))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{8 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}}{5 + \sqrt{41} + \frac{8 \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}} \right)}}{41} 
          /      ____              4            \
          |5 - \/ 41  + ------------------------|
          |             /      1   \    /    pi\|
          |             |1 + ------|*sec|x - --||
  ____    |             \    sec(x)/    \    2 /|
\/ 41 *log|-------------------------------------|
          |      ____              4            |
          |5 + \/ 41  + ------------------------|
          |             /      1   \    /    pi\|
          |             |1 + ------|*sec|x - --||
          \             \    sec(x)/    \    2 //
-------------------------------------------------
                        41
41log⁡(−41+5+4(1+1sec⁡(x))sec⁡(x−π2)5+41+4(1+1sec⁡(x))sec⁡(x−π2))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} + 5 + \frac{4}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}}{5 + \sqrt{41} + \frac{4}{\left(1 + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}} \right)}}{41} 
sqrt(41)*log((5 - sqrt(41) + 4/((1 + 1/sec(x))*sec(x - pi/2)))/(5 + sqrt(41) + 4/((1 + 1/sec(x))*sec(x - pi/2))))/41
Unión de expresiones racionales [src] 
          /                            ____             \
  ____    |5 + 4*sin(x) + 5*cos(x) - \/ 41 *(1 + cos(x))|
\/ 41 *log|---------------------------------------------|
          |                             /      ____\    |
          \     4*sin(x) + (1 + cos(x))*\5 + \/ 41 /    /
---------------------------------------------------------
                            41
41log⁡(−41(cos⁡(x)+1)+4sin⁡(x)+5cos⁡(x)+5(5+41)(cos⁡(x)+1)+4sin⁡(x))41\frac{\sqrt{41} \log{\left(\frac{- \sqrt{41} \left(\cos{\left(x \right)} + 1\right) + 4 \sin{\left(x \right)} + 5 \cos{\left(x \right)} + 5}{\left(5 + \sqrt{41}\right) \left(\cos{\left(x \right)} + 1\right) + 4 \sin{\left(x \right)}} \right)}}{41} 
sqrt(41)*log((5 + 4*sin(x) + 5*cos(x) - sqrt(41)*(1 + cos(x)))/(4*sin(x) + (1 + cos(x))*(5 + sqrt(41))))/41
    © Sr Examen – Калькулятор