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Simplificación de expresiones/ Descomposición en fracciones simples/ cot(x)^cot(pi/(4+x))*((-1-cot(pi/(4+x))^2)*log(cot(x))+(-1-cot(x)^2)*cot(pi/(4+x))/cot(x))

¿Cómo vas a descomponer esta cot(x)^cot(pi/(4+x))*((-1-cot(pi/(4+x))^2)*log(cot(x))+(-1-cot(x)^2)*cot(pi/(4+x))/cot(x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           /  pi \ /                                 /        2   \    /  pi \\
        cot|-----| |                                 \-1 - cot (x)/*cot|-----||
           \4 + x/ |/        2/  pi \\                                 \4 + x/|
(cot(x))          *||-1 - cot |-----||*log(cot(x)) + -------------------------|
                   \\         \4 + x//                         cot(x)         /
((−cot⁡2(x)−1)cot⁡(πx+4)cot⁡(x)+(−cot⁡2(πx+4)−1)log⁡(cot⁡(x)))cot⁡cot⁡(πx+4)(x)\left(\frac{\left(- \cot^{2}{\left(x \right)} - 1\right) \cot{\left(\frac{\pi}{x + 4} \right)}}{\cot{\left(x \right)}} + \left(- \cot^{2}{\left(\frac{\pi}{x + 4} \right)} - 1\right) \log{\left(\cot{\left(x \right)} \right)}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
cot(x)^cot(pi/(4 + x))*((-1 - cot(pi/(4 + x))^2)*log(cot(x)) + ((-1 - cot(x)^2)*cot(pi/(4 + x)))/cot(x))
Simplificación general [src] 
                 /  pi \ /   /  pi \                     \
         -1 + cot|-----| |cot|-----|                     |
                 \4 + x/ |   \4 + x/   cot(x)*log(cot(x))|
-(cot(x))               *|---------- + ------------------|
                         |    2              2/  pi \    |
                         | sin (x)        sin |-----|    |
                         \                    \4 + x/    /
−(log⁡(cot⁡(x))cot⁡(x)sin⁡2(πx+4)+cot⁡(πx+4)sin⁡2(x))cot⁡cot⁡(πx+4)−1(x)- \left(\frac{\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}} + \frac{\cot{\left(\frac{\pi}{x + 4} \right)}}{\sin^{2}{\left(x \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)} - 1}{\left(x \right)} 
-cot(x)^(-1 + cot(pi/(4 + x)))*(cot(pi/(4 + x))/sin(x)^2 + cot(x)*log(cot(x))/sin(pi/(4 + x))^2)
Respuesta numérica [src] 
cot(x)^cot(pi/(4 + x))*((-1.0 - cot(pi/(4 + x))^2)*log(cot(x)) + (-1.0 - cot(x)^2)*cot(pi/(4 + x))/cot(x))
cot(x)^cot(pi/(4 + x))*((-1.0 - cot(pi/(4 + x))^2)*log(cot(x)) + (-1.0 - cot(x)^2)*cot(pi/(4 + x))/cot(x))
Denominador racional [src] 
           /  pi \                                                                    
        cot|-----|                                                                    
           \4 + x/ //        2   \    /  pi \   /        2/  pi \\                   \
(cot(x))          *|\-1 - cot (x)/*cot|-----| + |-1 - cot |-----||*cot(x)*log(cot(x))|
                   \                  \4 + x/   \         \4 + x//                   /
--------------------------------------------------------------------------------------
                                        cot(x)
((−cot⁡2(x)−1)cot⁡(πx+4)+(−cot⁡2(πx+4)−1)log⁡(cot⁡(x))cot⁡(x))cot⁡cot⁡(πx+4)(x)cot⁡(x)\frac{\left(\left(- \cot^{2}{\left(x \right)} - 1\right) \cot{\left(\frac{\pi}{x + 4} \right)} + \left(- \cot^{2}{\left(\frac{\pi}{x + 4} \right)} - 1\right) \log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)}}{\cot{\left(x \right)}} 
cot(x)^cot(pi/(4 + x))*((-1 - cot(x)^2)*cot(pi/(4 + x)) + (-1 - cot(pi/(4 + x))^2)*cot(x)*log(cot(x)))/cot(x)
Unión de expresiones racionales [src] 
           /  pi \                                                                    
        cot|-----|                                                                    
           \4 + x/ //        2   \    /  pi \   /        2/  pi \\                   \
(cot(x))          *|\-1 - cot (x)/*cot|-----| + |-1 - cot |-----||*cot(x)*log(cot(x))|
                   \                  \4 + x/   \         \4 + x//                   /
--------------------------------------------------------------------------------------
                                        cot(x)
((−cot⁡2(x)−1)cot⁡(πx+4)+(−cot⁡2(πx+4)−1)log⁡(cot⁡(x))cot⁡(x))cot⁡cot⁡(πx+4)(x)cot⁡(x)\frac{\left(\left(- \cot^{2}{\left(x \right)} - 1\right) \cot{\left(\frac{\pi}{x + 4} \right)} + \left(- \cot^{2}{\left(\frac{\pi}{x + 4} \right)} - 1\right) \log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)}}{\cot{\left(x \right)}} 
cot(x)^cot(pi/(4 + x))*((-1 - cot(x)^2)*cot(pi/(4 + x)) + (-1 - cot(pi/(4 + x))^2)*cot(x)*log(cot(x)))/cot(x)
Denominador común [src] 
                                              /  pi \                                                                                               
                                           cot|-----|                                                                                               
             /  pi \                          \4 + x/    /  pi \              /  pi \                                      /  pi \                  
          cot|-----|               (cot(x))          *cot|-----|           cot|-----|                                   cot|-----|                  
             \4 + x/                                     \4 + x/              \4 + x/    2/  pi \                          \4 + x/           /  pi \
- (cot(x))          *log(cot(x)) - ----------------------------- - (cot(x))          *cot |-----|*log(cot(x)) - (cot(x))          *cot(x)*cot|-----|
                                               cot(x)                                     \4 + x/                                            \4 + x/
−log⁡(cot⁡(x))cot⁡cot⁡(πx+4)(x)cot⁡2(πx+4)−log⁡(cot⁡(x))cot⁡cot⁡(πx+4)(x)−cot⁡(x)cot⁡cot⁡(πx+4)(x)cot⁡(πx+4)−cot⁡cot⁡(πx+4)(x)cot⁡(πx+4)cot⁡(x)- \log{\left(\cot{\left(x \right)} \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot^{2}{\left(\frac{\pi}{x + 4} \right)} - \log{\left(\cot{\left(x \right)} \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} - \cot{\left(x \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot{\left(\frac{\pi}{x + 4} \right)} - \frac{\cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot{\left(\frac{\pi}{x + 4} \right)}}{\cot{\left(x \right)}} 
-cot(x)^cot(pi/(4 + x))*log(cot(x)) - cot(x)^cot(pi/(4 + x))*cot(pi/(4 + x))/cot(x) - cot(x)^cot(pi/(4 + x))*cot(pi/(4 + x))^2*log(cot(x)) - cot(x)^cot(pi/(4 + x))*cot(x)*cot(pi/(4 + x))
Abrimos la expresión [src] 
                                              /  pi \                                                                                               
                                           cot|-----|                                                                                               
             /  pi \                          \4 + x/    /  pi \              /  pi \                                      /  pi \                  
          cot|-----|               (cot(x))          *cot|-----|           cot|-----|                                   cot|-----|                  
             \4 + x/                                     \4 + x/              \4 + x/    2/  pi \                          \4 + x/           /  pi \
- (cot(x))          *log(cot(x)) - ----------------------------- - (cot(x))          *cot |-----|*log(cot(x)) - (cot(x))          *cot(x)*cot|-----|
                                               cot(x)                                     \4 + x/                                            \4 + x/
−log⁡(cot⁡(x))cot⁡cot⁡(πx+4)(x)cot⁡2(πx+4)−log⁡(cot⁡(x))cot⁡cot⁡(πx+4)(x)−cot⁡(x)cot⁡cot⁡(πx+4)(x)cot⁡(πx+4)−cot⁡cot⁡(πx+4)(x)cot⁡(πx+4)cot⁡(x)- \log{\left(\cot{\left(x \right)} \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot^{2}{\left(\frac{\pi}{x + 4} \right)} - \log{\left(\cot{\left(x \right)} \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} - \cot{\left(x \right)} \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot{\left(\frac{\pi}{x + 4} \right)} - \frac{\cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} \cot{\left(\frac{\pi}{x + 4} \right)}}{\cot{\left(x \right)}} 
-cot(x)^cot(pi/(4 + x))*log(cot(x)) - cot(x)^cot(pi/(4 + x))*cot(pi/(4 + x))/cot(x) - cot(x)^cot(pi/(4 + x))*cot(pi/(4 + x))^2*log(cot(x)) - cot(x)^cot(pi/(4 + x))*cot(x)*cot(pi/(4 + x))
Combinatoria [src] 
            /  pi \                                                                                         
         cot|-----|                                                                                         
            \4 + x/ /   2       /  pi \                           2/  pi \                         /  pi \\ 
-(cot(x))          *|cot (x)*cot|-----| + cot(x)*log(cot(x)) + cot |-----|*cot(x)*log(cot(x)) + cot|-----|| 
                    \           \4 + x/                            \4 + x/                         \4 + x// 
------------------------------------------------------------------------------------------------------------
                                                   cot(x)
−(log⁡(cot⁡(x))cot⁡(x)cot⁡2(πx+4)+log⁡(cot⁡(x))cot⁡(x)+cot⁡2(x)cot⁡(πx+4)+cot⁡(πx+4))cot⁡cot⁡(πx+4)(x)cot⁡(x)- \frac{\left(\log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)} \cot^{2}{\left(\frac{\pi}{x + 4} \right)} + \log{\left(\cot{\left(x \right)} \right)} \cot{\left(x \right)} + \cot^{2}{\left(x \right)} \cot{\left(\frac{\pi}{x + 4} \right)} + \cot{\left(\frac{\pi}{x + 4} \right)}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)}}{\cot{\left(x \right)}} 
-cot(x)^cot(pi/(4 + x))*(cot(x)^2*cot(pi/(4 + x)) + cot(x)*log(cot(x)) + cot(pi/(4 + x))^2*cot(x)*log(cot(x)) + cot(pi/(4 + x)))/cot(x)
Parte trigonométrica [src] 
            1                                                              
        ----------                                                         
           /  pi \ /                                 /        1   \       \
        tan|-----| |                                 |-1 - -------|*tan(x)|
           \4 + x/ |                                 |        2   |       |
/  1   \           |/          1     \    /  1   \   \     tan (x)/       |
|------|          *||-1 - -----------|*log|------| + ---------------------|
\tan(x)/           ||        2/  pi \|    \tan(x)/            /  pi \     |
                   ||     tan |-----||                     tan|-----|     |
                   \\         \4 + x//                        \4 + x/     /
((−1−1tan⁡2(x))tan⁡(x)tan⁡(πx+4)+(−1−1tan⁡2(πx+4))log⁡(1tan⁡(x)))(1tan⁡(x))1tan⁡(πx+4)\left(\frac{\left(-1 - \frac{1}{\tan^{2}{\left(x \right)}}\right) \tan{\left(x \right)}}{\tan{\left(\frac{\pi}{x + 4} \right)}} + \left(-1 - \frac{1}{\tan^{2}{\left(\frac{\pi}{x + 4} \right)}}\right) \log{\left(\frac{1}{\tan{\left(x \right)}} \right)}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
            1                                                       
        ----------                                                  
           /  pi \                                                  
        tan|-----|                                                  
           \4 + x/                                                  
/  1   \           /     2/  pi \    /  1   \            2         \
|------|          *|- csc |-----|*log|------| - -------------------|
\tan(x)/           |      \4 + x/    \tan(x)/               /  pi \|
                   |                            sin(2*x)*tan|-----||
                   \                                        \4 + x//
(−log⁡(1tan⁡(x))csc⁡2(πx+4)−2sin⁡(2x)tan⁡(πx+4))(1tan⁡(x))1tan⁡(πx+4)\left(- \log{\left(\frac{1}{\tan{\left(x \right)}} \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)} - \frac{2}{\sin{\left(2 x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
               1                                            
           ----------                                       
              /  pi \                                       
           tan|-----| /    /  1   \                        \
              \4 + x/ | log|------|                        |
   /  1   \           |    \tan(x)/              1         |
-2*|------|          *|-------------- + -------------------|
   \tan(x)/           |       / 2*pi\               /  pi \|
                      |1 - cos|-----|   sin(2*x)*tan|-----||
                      \       \4 + x/               \4 + x//
−2(1sin⁡(2x)tan⁡(πx+4)+log⁡(1tan⁡(x))1−cos⁡(2πx+4))(1tan⁡(x))1tan⁡(πx+4)- 2 \left(\frac{1}{\sin{\left(2 x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}} + \frac{\log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{1 - \cos{\left(\frac{2 \pi}{x + 4} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
                / 2*pi\                                           
             sin|-----|                                           
                \4 + x/                                           
           -------------                                          
                2/  pi \ /     / sin(2*x)\                       \
           2*sin |-----| |  log|---------|           / 2*pi\     |
                 \4 + x/ |     |     2   |        sin|-----|     |
/ sin(2*x)\              |     \2*sin (x)/           \4 + x/     |
|---------|             *|- -------------- - --------------------|
|     2   |              |      2/  pi \                 2/  pi \|
\2*sin (x)/              |   sin |-----|     sin(2*x)*sin |-----||
                         \       \4 + x/                  \4 + x//
(sin⁡(2x)2sin⁡2(x))sin⁡(2πx+4)2sin⁡2(πx+4)(−log⁡(sin⁡(2x)2sin⁡2(x))sin⁡2(πx+4)−sin⁡(2πx+4)sin⁡(2x)sin⁡2(πx+4))\left(\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right)^{\frac{\sin{\left(\frac{2 \pi}{x + 4} \right)}}{2 \sin^{2}{\left(\frac{\pi}{x + 4} \right)}}} \left(- \frac{\log{\left(\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}} \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}} - \frac{\sin{\left(\frac{2 \pi}{x + 4} \right)}}{\sin{\left(2 x \right)} \sin^{2}{\left(\frac{\pi}{x + 4} \right)}}\right) 
                    /  pi \                                                             
                 cos|-----|                                                             
                    \4 + x/                                                             
             ----------------- /      /   cos(x)  \                                    \
                /  pi     pi \ |   log|-----------|                                    |
             cos|- -- + -----| |      |   /    pi\|              /  pi    2*pi\        |
                \  2    4 + x/ |      |cos|x - --||           cos|- -- + -----|        |
/   cos(x)  \                  |      \   \    2 //              \  2    4 + x/        |
|-----------|                 *|- ------------------ - --------------------------------|
|   /    pi\|                  |     2/  pi     pi \      /      pi\    2/  pi     pi \|
|cos|x - --||                  |  cos |- -- + -----|   cos|2*x - --|*cos |- -- + -----||
\   \    2 //                  \      \  2    4 + x/      \      2 /     \  2    4 + x//
(cos⁡(x)cos⁡(x−π2))cos⁡(πx+4)cos⁡(−π2+πx+4)(−log⁡(cos⁡(x)cos⁡(x−π2))cos⁡2(−π2+πx+4)−cos⁡(−π2+2πx+4)cos⁡2(−π2+πx+4)cos⁡(2x−π2))\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}}\right)^{\frac{\cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}} \left(- \frac{\log{\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}} - \frac{\cos{\left(- \frac{\pi}{2} + \frac{2 \pi}{x + 4} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} \cos{\left(2 x - \frac{\pi}{2} \right)}}\right) 
                / 2*pi\                                                                             
             sin|-----|                                                                             
                \4 + x/                                                                             
           ------------- /                                              /        2     \           \
                2/  pi \ |                                         2    |     sin (2*x)|    / 2*pi\|
           2*sin |-----| |/         2/ 2*pi\ \                  sin (x)*|-1 - ---------|*sin|-----||
                 \4 + x/ ||      sin |-----| |                          |          4   |    \4 + x/|
/ sin(2*x)\              ||          \4 + x/ |    / sin(2*x)\           \     4*sin (x)/           |
|---------|             *||-1 - -------------|*log|---------| + -----------------------------------|
|     2   |              ||          4/  pi \|    |     2   |                       2/  pi \       |
\2*sin (x)/              ||     4*sin |-----||    \2*sin (x)/           sin(2*x)*sin |-----|       |
                         \\           \4 + x//                                       \4 + x/       /
(sin⁡(2x)2sin⁡2(x))sin⁡(2πx+4)2sin⁡2(πx+4)((−1−sin⁡2(2x)4sin⁡4(x))sin⁡2(x)sin⁡(2πx+4)sin⁡(2x)sin⁡2(πx+4)+(−1−sin⁡2(2πx+4)4sin⁡4(πx+4))log⁡(sin⁡(2x)2sin⁡2(x)))\left(\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right)^{\frac{\sin{\left(\frac{2 \pi}{x + 4} \right)}}{2 \sin^{2}{\left(\frac{\pi}{x + 4} \right)}}} \left(\frac{\left(-1 - \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}\right) \sin^{2}{\left(x \right)} \sin{\left(\frac{2 \pi}{x + 4} \right)}}{\sin{\left(2 x \right)} \sin^{2}{\left(\frac{\pi}{x + 4} \right)}} + \left(-1 - \frac{\sin^{2}{\left(\frac{2 \pi}{x + 4} \right)}}{4 \sin^{4}{\left(\frac{\pi}{x + 4} \right)}}\right) \log{\left(\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}} \right)}\right) 
            1                                                                
        ----------                                                           
           /  pi \                                                           
        tan|-----| /                    /  pi \                    /  1   \ \
           \4 + x/ |               4*cos|-----|               2*log|------| |
/  1   \           |                    \4 + x/                    \tan(x)/ |
|------|          *|- ------------------------------------- - --------------|
\tan(x)/           |       /        pi \      /        pi \          / 2*pi\|
                   |  - cos|2*x + -----| + cos|2*x - -----|   1 - cos|-----||
                   \       \      4 + x/      \      4 + x/          \4 + x//
(−4cos⁡(πx+4)cos⁡(2x−πx+4)−cos⁡(2x+πx+4)−2log⁡(1tan⁡(x))1−cos⁡(2πx+4))(1tan⁡(x))1tan⁡(πx+4)\left(- \frac{4 \cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(2 x - \frac{\pi}{x + 4} \right)} - \cos{\left(2 x + \frac{\pi}{x + 4} \right)}} - \frac{2 \log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{1 - \cos{\left(\frac{2 \pi}{x + 4} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
                   /                       2                                    2                         \
           /  pi \ |  /       2/    pi   \\                /       2/    pi   \\  /       2   \    /  pi \|
        cot|-----| |  |1 + cot |---------|| *log(cot(x))   |1 + cot |---------|| *\1 + cot (x)/*cot|-----||
           \4 + x/ |  \        \2*(4 + x)//                \        \2*(4 + x)//                   \4 + x/|
(cot(x))          *|- ---------------------------------- - -----------------------------------------------|
                   |               2/    pi   \                 /       2/  pi \\           2/    pi   \  |
                   |          4*cot |---------|               4*|1 + cot |-----||*cot(x)*cot |---------|  |
                   \                \2*(4 + x)/                 \        \4 + x//            \2*(4 + x)/  /
(−(cot⁡2(x)+1)(cot⁡2(π2(x+4))+1)2cot⁡(πx+4)4(cot⁡2(πx+4)+1)cot⁡(x)cot⁡2(π2(x+4))−(cot⁡2(π2(x+4))+1)2log⁡(cot⁡(x))4cot⁡2(π2(x+4)))cot⁡cot⁡(πx+4)(x)\left(- \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \cot{\left(\frac{\pi}{x + 4} \right)}}{4 \left(\cot^{2}{\left(\frac{\pi}{x + 4} \right)} + 1\right) \cot{\left(x \right)} \cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}} - \frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \log{\left(\cot{\left(x \right)} \right)}}{4 \cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
            1                                            
        ----------                                       
           /  pi \                                       
        tan|-----| /     /  1   \           / 2*pi\     \
           \4 + x/ |  log|------|        sin|-----|     |
/  1   \           |     \tan(x)/           \4 + x/     |
|------|          *|- ----------- - --------------------|
\tan(x)/           |     2/  pi \               2/  pi \|
                   |  sin |-----|   sin(2*x)*sin |-----||
                   \      \4 + x/                \4 + x//
(−log⁡(1tan⁡(x))sin⁡2(πx+4)−sin⁡(2πx+4)sin⁡(2x)sin⁡2(πx+4))(1tan⁡(x))1tan⁡(πx+4)\left(- \frac{\log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}} - \frac{\sin{\left(\frac{2 \pi}{x + 4} \right)}}{\sin{\left(2 x \right)} \sin^{2}{\left(\frac{\pi}{x + 4} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
           /  pi \                                      
        cot|-----|                                      
           \4 + x/ /  log(cot(x))            2         \
(cot(x))          *|- ----------- - -------------------|
                   |     2/  pi \               /  pi \|
                   |  sin |-----|   sin(2*x)*tan|-----||
                   \      \4 + x/               \4 + x//
(−log⁡(cot⁡(x))sin⁡2(πx+4)−2sin⁡(2x)tan⁡(πx+4))cot⁡cot⁡(πx+4)(x)\left(- \frac{\log{\left(\cot{\left(x \right)} \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}} - \frac{2}{\sin{\left(2 x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
           /  pi \ /                    /  pi \                    /  1   \ \
        cot|-----| |               4*cos|-----|               2*log|------| |
           \4 + x/ |                    \4 + x/                    \tan(x)/ |
(cot(x))          *|- ------------------------------------- - --------------|
                   |       /        pi \      /        pi \          / 2*pi\|
                   |  - cos|2*x + -----| + cos|2*x - -----|   1 - cos|-----||
                   \       \      4 + x/      \      4 + x/          \4 + x//
(−4cos⁡(πx+4)cos⁡(2x−πx+4)−cos⁡(2x+πx+4)−2log⁡(1tan⁡(x))1−cos⁡(2πx+4))cot⁡cot⁡(πx+4)(x)\left(- \frac{4 \cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(2 x - \frac{\pi}{x + 4} \right)} - \cos{\left(2 x + \frac{\pi}{x + 4} \right)}} - \frac{2 \log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{1 - \cos{\left(\frac{2 \pi}{x + 4} \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
                   /                                                  2            \
           /  pi \ |  /       2   \    /  pi \   /       2/    pi   \\             |
        cot|-----| |  \1 + cot (x)/*cot|-----|   |1 + cot |---------|| *log(cot(x))|
           \4 + x/ |                   \4 + x/   \        \2*(4 + x)//             |
(cot(x))          *|- ------------------------ - ----------------------------------|
                   |           cot(x)                         2/    pi   \         |
                   |                                     4*cot |---------|         |
                   \                                           \2*(4 + x)/         /
(−(cot⁡2(x)+1)cot⁡(πx+4)cot⁡(x)−(cot⁡2(π2(x+4))+1)2log⁡(cot⁡(x))4cot⁡2(π2(x+4)))cot⁡cot⁡(πx+4)(x)\left(- \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{\pi}{x + 4} \right)}}{\cot{\left(x \right)}} - \frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \log{\left(\cot{\left(x \right)} \right)}}{4 \cot^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
              /  pi \ /    /  1   \                        \
           cot|-----| | log|------|                        |
              \4 + x/ |    \tan(x)/              1         |
-2*(cot(x))          *|-------------- + -------------------|
                      |       / 2*pi\               /  pi \|
                      |1 - cos|-----|   sin(2*x)*tan|-----||
                      \       \4 + x/               \4 + x//
−2(1sin⁡(2x)tan⁡(πx+4)+log⁡(1tan⁡(x))1−cos⁡(2πx+4))cot⁡cot⁡(πx+4)(x)- 2 \left(\frac{1}{\sin{\left(2 x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}} + \frac{\log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{1 - \cos{\left(\frac{2 \pi}{x + 4} \right)}}\right) \cot^{\cot{\left(\frac{\pi}{x + 4} \right)}}{\left(x \right)} 
                    /  pi \                                                            
                 cos|-----|                                                            
                    \4 + x/                                                            
             ----------------- /      /   cos(x)  \                                   \
                /  pi     pi \ |   log|-----------|                                   |
             cos|- -- + -----| |      |   /    pi\|                   /  pi \         |
                \  2    4 + x/ |      |cos|x - --||              2*cos|-----|         |
/   cos(x)  \                  |      \   \    2 //                   \4 + x/         |
|-----------|                 *|- ------------------ - -------------------------------|
|   /    pi\|                  |     2/  pi     pi \      /      pi\    /  pi     pi \|
|cos|x - --||                  |  cos |- -- + -----|   cos|2*x - --|*cos|- -- + -----||
\   \    2 //                  \      \  2    4 + x/      \      2 /    \  2    4 + x//
(cos⁡(x)cos⁡(x−π2))cos⁡(πx+4)cos⁡(−π2+πx+4)(−log⁡(cos⁡(x)cos⁡(x−π2))cos⁡2(−π2+πx+4)−2cos⁡(πx+4)cos⁡(−π2+πx+4)cos⁡(2x−π2))\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}}\right)^{\frac{\cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}} \left(- \frac{\log{\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}} - \frac{2 \cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} \cos{\left(2 x - \frac{\pi}{2} \right)}}\right) 
                   /  pi \                                                           
                csc|-----|                                                           
                   \4 + x/                                                           
             ---------------                                                         
                /pi     pi \                                                         
             csc|-- - -----| /                                               /  pi \\
                \2    4 + x/ |                                 2*csc(2*x)*csc|-----||
/   csc(x)  \                |     2/  pi \    /   csc(x)  \                 \4 + x/|
|-----------|               *|- csc |-----|*log|-----------| - ---------------------|
|   /pi    \|                |      \4 + x/    |   /pi    \|         /pi     pi \   |
|csc|-- - x||                |                 |csc|-- - x||      csc|-- - -----|   |
\   \2     //                \                 \   \2     //         \2    4 + x/   /
(csc⁡(x)csc⁡(−x+π2))csc⁡(πx+4)csc⁡(π2−πx+4)(−log⁡(csc⁡(x)csc⁡(−x+π2))csc⁡2(πx+4)−2csc⁡(2x)csc⁡(πx+4)csc⁡(π2−πx+4))\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\frac{\csc{\left(\frac{\pi}{x + 4} \right)}}{\csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}}} \left(- \log{\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)} - \frac{2 \csc{\left(2 x \right)} \csc{\left(\frac{\pi}{x + 4} \right)}}{\csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}}\right) 
                   /  pi \                                                          
                csc|-----|                                                          
                   \4 + x/                                                          
             ---------------                                                        
                /pi     pi \                                                        
             csc|-- - -----| /                                    2/  pi \         \
                \2    4 + x/ |                                 csc |-----|*csc(2*x)|
/   csc(x)  \                |     2/  pi \    /   csc(x)  \       \4 + x/         |
|-----------|               *|- csc |-----|*log|-----------| - --------------------|
|   /pi    \|                |      \4 + x/    |   /pi    \|           / 2*pi\     |
|csc|-- - x||                |                 |csc|-- - x||        csc|-----|     |
\   \2     //                \                 \   \2     //           \4 + x/     /
(csc⁡(x)csc⁡(−x+π2))csc⁡(πx+4)csc⁡(π2−πx+4)(−log⁡(csc⁡(x)csc⁡(−x+π2))csc⁡2(πx+4)−csc⁡(2x)csc⁡2(πx+4)csc⁡(2πx+4))\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\frac{\csc{\left(\frac{\pi}{x + 4} \right)}}{\csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}}} \left(- \log{\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)} - \frac{\csc{\left(2 x \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)}}{\csc{\left(\frac{2 \pi}{x + 4} \right)}}\right) 
                   /  pi \                                                                                          
                csc|-----|                                                                                          
                   \4 + x/   /                                           /          2      \                       \
             --------------- |                                           |       csc (x)   |    /  pi \    /pi    \|
                /pi     pi \ |                                           |-1 - ------------|*csc|-----|*csc|-- - x||
             csc|-- - -----| |/          2/  pi \   \                    |        2/pi    \|    \4 + x/    \2     /|
                \2    4 + x/ ||       csc |-----|   |                    |     csc |-- - x||                       |
/   csc(x)  \                ||           \4 + x/   |    /   csc(x)  \   \         \2     //                       |
|-----------|               *||-1 - ----------------|*log|-----------| + ------------------------------------------|
|   /pi    \|                ||        2/pi     pi \|    |   /pi    \|                       /pi     pi \          |
|csc|-- - x||                ||     csc |-- - -----||    |csc|-- - x||             csc(x)*csc|-- - -----|          |
\   \2     //                \\         \2    4 + x//    \   \2     //                       \2    4 + x/          /
(csc⁡(x)csc⁡(−x+π2))csc⁡(πx+4)csc⁡(π2−πx+4)((−csc⁡2(x)csc⁡2(−x+π2)−1)csc⁡(πx+4)csc⁡(−x+π2)csc⁡(x)csc⁡(π2−πx+4)+(−csc⁡2(πx+4)csc⁡2(π2−πx+4)−1)log⁡(csc⁡(x)csc⁡(−x+π2)))\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{\frac{\csc{\left(\frac{\pi}{x + 4} \right)}}{\csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}}} \left(\frac{\left(- \frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - 1\right) \csc{\left(\frac{\pi}{x + 4} \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}} + \left(- \frac{\csc^{2}{\left(\frac{\pi}{x + 4} \right)}}{\csc^{2}{\left(\frac{\pi}{2} - \frac{\pi}{x + 4} \right)}} - 1\right) \log{\left(\frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} \right)}\right) 
            1                                                                                              
        ----------                                                                                         
           /  pi \ /                       2                                    2                         \
        tan|-----| |  /       2/    pi   \\     /  1   \   /       2/    pi   \\  /       2   \    /  pi \|
           \4 + x/ |  |1 + tan |---------|| *log|------|   |1 + tan |---------|| *\1 + tan (x)/*tan|-----||
/  1   \           |  \        \2*(4 + x)//     \tan(x)/   \        \2*(4 + x)//                   \4 + x/|
|------|          *|- ---------------------------------- - -----------------------------------------------|
\tan(x)/           |               2/    pi   \                 /       2/  pi \\           2/    pi   \  |
                   |          4*tan |---------|               4*|1 + tan |-----||*tan(x)*tan |---------|  |
                   \                \2*(4 + x)/                 \        \4 + x//            \2*(4 + x)/  /
(−(tan⁡2(x)+1)(tan⁡2(π2(x+4))+1)2tan⁡(πx+4)4(tan⁡2(πx+4)+1)tan⁡(x)tan⁡2(π2(x+4))−(tan⁡2(π2(x+4))+1)2log⁡(1tan⁡(x))4tan⁡2(π2(x+4)))(1tan⁡(x))1tan⁡(πx+4)\left(- \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \tan{\left(\frac{\pi}{x + 4} \right)}}{4 \left(\tan^{2}{\left(\frac{\pi}{x + 4} \right)} + 1\right) \tan{\left(x \right)} \tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}} - \frac{\left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{4 \tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
            1                                                                   
        ----------                                                              
           /  pi \                                                              
        tan|-----|                                                              
           \4 + x/                                                              
/  1   \           /     2/  pi \    /  1   \      2/  pi \             / 2*pi\\
|------|          *|- csc |-----|*log|------| - csc |-----|*csc(2*x)*sin|-----||
\tan(x)/           \      \4 + x/    \tan(x)/       \4 + x/             \4 + x//
(−log⁡(1tan⁡(x))csc⁡2(πx+4)−sin⁡(2πx+4)csc⁡(2x)csc⁡2(πx+4))(1tan⁡(x))1tan⁡(πx+4)\left(- \log{\left(\frac{1}{\tan{\left(x \right)}} \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)} - \sin{\left(\frac{2 \pi}{x + 4} \right)} \csc{\left(2 x \right)} \csc^{2}{\left(\frac{\pi}{x + 4} \right)}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
           /  pi \                                                                    
        csc|-----|                                                                    
           \4 + x/                                                                    
        ---------- /                                 /        2   \                  \
           /  pi \ |                                 |     csc (x)|    /  pi \       |
        sec|-----| |/        2/  pi \\               |-1 - -------|*csc|-----|*sec(x)|
           \4 + x/ ||     csc |-----||               |        2   |    \4 + x/       |
/csc(x)\           ||         \4 + x/|    /csc(x)\   \     sec (x)/                  |
|------|          *||-1 - -----------|*log|------| + --------------------------------|
\sec(x)/           ||        2/  pi \|    \sec(x)/                    /  pi \        |
                   ||     sec |-----||                      csc(x)*sec|-----|        |
                   \\         \4 + x//                                \4 + x/        /
(csc⁡(x)sec⁡(x))csc⁡(πx+4)sec⁡(πx+4)((−csc⁡2(x)sec⁡2(x)−1)csc⁡(πx+4)sec⁡(x)csc⁡(x)sec⁡(πx+4)+(−csc⁡2(πx+4)sec⁡2(πx+4)−1)log⁡(csc⁡(x)sec⁡(x)))\left(\frac{\csc{\left(x \right)}}{\sec{\left(x \right)}}\right)^{\frac{\csc{\left(\frac{\pi}{x + 4} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)}}} \left(\frac{\left(- \frac{\csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} - 1\right) \csc{\left(\frac{\pi}{x + 4} \right)} \sec{\left(x \right)}}{\csc{\left(x \right)} \sec{\left(\frac{\pi}{x + 4} \right)}} + \left(- \frac{\csc^{2}{\left(\frac{\pi}{x + 4} \right)}}{\sec^{2}{\left(\frac{\pi}{x + 4} \right)}} - 1\right) \log{\left(\frac{\csc{\left(x \right)}}{\sec{\left(x \right)}} \right)}\right) 
           /  pi \                                                                    
        cos|-----|                                                                    
           \4 + x/                                                                    
        ---------- /                                 /        2   \                  \
           /  pi \ |                                 |     cos (x)|    /  pi \       |
        sin|-----| |/        2/  pi \\               |-1 - -------|*cos|-----|*sin(x)|
           \4 + x/ ||     cos |-----||               |        2   |    \4 + x/       |
/cos(x)\           ||         \4 + x/|    /cos(x)\   \     sin (x)/                  |
|------|          *||-1 - -----------|*log|------| + --------------------------------|
\sin(x)/           ||        2/  pi \|    \sin(x)/                    /  pi \        |
                   ||     sin |-----||                      cos(x)*sin|-----|        |
                   \\         \4 + x//                                \4 + x/        /
(cos⁡(x)sin⁡(x))cos⁡(πx+4)sin⁡(πx+4)((−1−cos⁡2(x)sin⁡2(x))sin⁡(x)cos⁡(πx+4)sin⁡(πx+4)cos⁡(x)+(−1−cos⁡2(πx+4)sin⁡2(πx+4))log⁡(cos⁡(x)sin⁡(x)))\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{\frac{\cos{\left(\frac{\pi}{x + 4} \right)}}{\sin{\left(\frac{\pi}{x + 4} \right)}}} \left(\frac{\left(-1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)} \cos{\left(\frac{\pi}{x + 4} \right)}}{\sin{\left(\frac{\pi}{x + 4} \right)} \cos{\left(x \right)}} + \left(-1 - \frac{\cos^{2}{\left(\frac{\pi}{x + 4} \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}}\right) \log{\left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} \right)}\right) 
                /  pi     pi \                                                                           
             sec|- -- + -----|                                                                           
                \  2    4 + x/                                                                           
             -----------------                                                                           
                    /  pi \                                                                              
                 sec|-----|                                                                              
                    \4 + x/                                                                              
/   /    pi\\                  /                        /   /    pi\\      2/  pi     pi \    /      pi\\
|sec|x - --||                  |                        |sec|x - --||   sec |- -- + -----|*sec|2*x - --||
|   \    2 /|                  |     2/  pi     pi \    |   \    2 /|       \  2    4 + x/    \      2 /|
|-----------|                 *|- sec |- -- + -----|*log|-----------| - --------------------------------|
\   sec(x)  /                  |      \  2    4 + x/    \   sec(x)  /             /  pi    2*pi\        |
                               |                                               sec|- -- + -----|        |
                               \                                                  \  2    4 + x/        /
(sec⁡(x−π2)sec⁡(x))sec⁡(−π2+πx+4)sec⁡(πx+4)(−log⁡(sec⁡(x−π2)sec⁡(x))sec⁡2(−π2+πx+4)−sec⁡2(−π2+πx+4)sec⁡(2x−π2)sec⁡(−π2+2πx+4))\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)^{\frac{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)}}} \left(- \log{\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} \right)} \sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} - \frac{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{2 \pi}{x + 4} \right)}}\right) 
            1                                                                
        ----------                                                           
           /  pi \ /                                           2            \
        tan|-----| |                      /       2/    pi   \\     /  1   \|
           \4 + x/ |            2         |1 + tan |---------|| *log|------||
/  1   \           |     1 + tan (x)      \        \2*(4 + x)//     \tan(x)/|
|------|          *|- ----------------- - ----------------------------------|
\tan(x)/           |            /  pi \                2/    pi   \         |
                   |  tan(x)*tan|-----|           4*tan |---------|         |
                   \            \4 + x/                 \2*(4 + x)/         /
(−tan⁡2(x)+1tan⁡(x)tan⁡(πx+4)−(tan⁡2(π2(x+4))+1)2log⁡(1tan⁡(x))4tan⁡2(π2(x+4)))(1tan⁡(x))1tan⁡(πx+4)\left(- \frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}} - \frac{\left(\tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)} + 1\right)^{2} \log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{4 \tan^{2}{\left(\frac{\pi}{2 \left(x + 4\right)} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
                    /  pi \                                                                                             
                 cos|-----|                                                                                             
                    \4 + x/    /                                             /          2      \                       \
             ----------------- |                                             |       cos (x)   |    /  pi \    /    pi\|
                /  pi     pi \ |                                             |-1 - ------------|*cos|-----|*cos|x - --||
             cos|- -- + -----| |/           2/  pi \    \                    |        2/    pi\|    \4 + x/    \    2 /|
                \  2    4 + x/ ||        cos |-----|    |                    |     cos |x - --||                       |
/   cos(x)  \                  ||            \4 + x/    |    /   cos(x)  \   \         \    2 //                       |
|-----------|                 *||-1 - ------------------|*log|-----------| + ------------------------------------------|
|   /    pi\|                  ||        2/  pi     pi \|    |   /    pi\|                      /  pi     pi \         |
|cos|x - --||                  ||     cos |- -- + -----||    |cos|x - --||            cos(x)*cos|- -- + -----|         |
\   \    2 //                  \\         \  2    4 + x//    \   \    2 //                      \  2    4 + x/         /
(cos⁡(x)cos⁡(x−π2))cos⁡(πx+4)cos⁡(−π2+πx+4)((−cos⁡2(x)cos⁡2(x−π2)−1)cos⁡(πx+4)cos⁡(x−π2)cos⁡(x)cos⁡(−π2+πx+4)+(−cos⁡2(πx+4)cos⁡2(−π2+πx+4)−1)log⁡(cos⁡(x)cos⁡(x−π2)))\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}}\right)^{\frac{\cos{\left(\frac{\pi}{x + 4} \right)}}{\cos{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}} \left(\frac{\left(- \frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - 1\right) \cos{\left(\frac{\pi}{x + 4} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}} + \left(- \frac{\cos^{2}{\left(\frac{\pi}{x + 4} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}} - 1\right) \log{\left(\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} \right)}\right) 
                /  pi     pi \                                                                                            
             sec|- -- + -----|                                                                                            
                \  2    4 + x/                                                                                            
             -----------------                                                                                            
                    /  pi \    /                                             /        2/    pi\\                         \
                 sec|-----|    |                                             |     sec |x - --||                         |
                    \4 + x/    |                                             |         \    2 /|           /  pi     pi \|
/   /    pi\\                  |/        2/  pi     pi \\    /   /    pi\\   |-1 - ------------|*sec(x)*sec|- -- + -----||
|sec|x - --||                  ||     sec |- -- + -----||    |sec|x - --||   |          2      |           \  2    4 + x/|
|   \    2 /|                  ||         \  2    4 + x/|    |   \    2 /|   \       sec (x)   /                         |
|-----------|                 *||-1 - ------------------|*log|-----------| + --------------------------------------------|
\   sec(x)  /                  ||           2/  pi \    |    \   sec(x)  /                 /  pi \    /    pi\           |
                               ||        sec |-----|    |                               sec|-----|*sec|x - --|           |
                               \\            \4 + x/    /                                  \4 + x/    \    2 /           /
(sec⁡(x−π2)sec⁡(x))sec⁡(−π2+πx+4)sec⁡(πx+4)((−1−sec⁡2(x−π2)sec⁡2(x))sec⁡(x)sec⁡(−π2+πx+4)sec⁡(πx+4)sec⁡(x−π2)+(−1−sec⁡2(−π2+πx+4)sec⁡2(πx+4))log⁡(sec⁡(x−π2)sec⁡(x)))\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)^{\frac{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)}}} \left(\frac{\left(-1 - \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right) \sec{\left(x \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)} \sec{\left(x - \frac{\pi}{2} \right)}} + \left(-1 - \frac{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}{\sec^{2}{\left(\frac{\pi}{x + 4} \right)}}\right) \log{\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} \right)}\right) 
                /  pi     pi \                                                                            
             sec|- -- + -----|                                                                            
                \  2    4 + x/                                                                            
             -----------------                                                                            
                    /  pi \                                                                               
                 sec|-----|                                                                               
                    \4 + x/                                                                               
/   /    pi\\                  /                        /   /    pi\\        /      pi\    /  pi     pi \\
|sec|x - --||                  |                        |sec|x - --||   2*sec|2*x - --|*sec|- -- + -----||
|   \    2 /|                  |     2/  pi     pi \    |   \    2 /|        \      2 /    \  2    4 + x/|
|-----------|                 *|- sec |- -- + -----|*log|-----------| - ---------------------------------|
\   sec(x)  /                  |      \  2    4 + x/    \   sec(x)  /                  /  pi \           |
                               |                                                    sec|-----|           |
                               \                                                       \4 + x/           /
(sec⁡(x−π2)sec⁡(x))sec⁡(−π2+πx+4)sec⁡(πx+4)(−log⁡(sec⁡(x−π2)sec⁡(x))sec⁡2(−π2+πx+4)−2sec⁡(−π2+πx+4)sec⁡(2x−π2)sec⁡(πx+4))\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)^{\frac{\sec{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)}}} \left(- \log{\left(\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}} \right)} \sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} - \frac{2 \sec{\left(- \frac{\pi}{2} + \frac{\pi}{x + 4} \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sec{\left(\frac{\pi}{x + 4} \right)}}\right) 
            1                                           
        ----------                                      
           /  pi \                                      
        tan|-----| /     /  1   \                      \
           \4 + x/ |  log|------|                      |
/  1   \           |     \tan(x)/            2         |
|------|          *|- ----------- - -------------------|
\tan(x)/           |     2/  pi \               /  pi \|
                   |  sin |-----|   sin(2*x)*tan|-----||
                   \      \4 + x/               \4 + x//
(−log⁡(1tan⁡(x))sin⁡2(πx+4)−2sin⁡(2x)tan⁡(πx+4))(1tan⁡(x))1tan⁡(πx+4)\left(- \frac{\log{\left(\frac{1}{\tan{\left(x \right)}} \right)}}{\sin^{2}{\left(\frac{\pi}{x + 4} \right)}} - \frac{2}{\sin{\left(2 x \right)} \tan{\left(\frac{\pi}{x + 4} \right)}}\right) \left(\frac{1}{\tan{\left(x \right)}}\right)^{\frac{1}{\tan{\left(\frac{\pi}{x + 4} \right)}}} 
(1/tan(x))^(1/tan(pi/(4 + x)))*(-log(1/tan(x))/sin(pi/(4 + x))^2 - 2/(sin(2*x)*tan(pi/(4 + x))))
    © Sr Examen – Калькулятор