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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(x)^(1/cos(x))*((1+tan(x)^2)/(cos(x)*tan(x))+log(tan(x))*sin(x)/cos(x)^2)

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

Expresión a simplificar:

Solución

Ha introducido [src] 
          1                                        
        ------ /        2                         \
        cos(x) | 1 + tan (x)    log(tan(x))*sin(x)|
(tan(x))      *|------------- + ------------------|
               |cos(x)*tan(x)           2         |
               \                     cos (x)      /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+tan⁡2(x)+1cos⁡(x)tan⁡(x))tan⁡1cos⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1}{\cos{\left(x \right)} \tan{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
tan(x)^(1/cos(x))*((1 + tan(x)^2)/((cos(x)*tan(x))) + (log(tan(x))*sin(x))/cos(x)^2)
Simplificación general [src] 
               1                             
        -1 + ------                          
             cos(x) /       2               \
(tan(x))           *\1 + sin (x)*log(tan(x))/
---------------------------------------------
                      3                      
                   cos (x)
(log⁡(tan⁡(x))sin⁡2(x)+1)tan⁡−1+1cos⁡(x)(x)cos⁡3(x)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin^{2}{\left(x \right)} + 1\right) \tan^{-1 + \frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{3}{\left(x \right)}} 
tan(x)^(-1 + 1/cos(x))*(1 + sin(x)^2*log(tan(x)))/cos(x)^3
Denominador racional [src] 
          1                                                              
        ------                                                           
        cos(x) /   2    /       2   \                                   \
(tan(x))      *\cos (x)*\1 + tan (x)/ + cos(x)*log(tan(x))*sin(x)*tan(x)/
-------------------------------------------------------------------------
                                 3                                       
                              cos (x)*tan(x)
((tan⁡2(x)+1)cos⁡2(x)+log⁡(tan⁡(x))sin⁡(x)cos⁡(x)tan⁡(x))tan⁡1cos⁡(x)(x)cos⁡3(x)tan⁡(x)\frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \cos^{2}{\left(x \right)} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(x \right)}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{3}{\left(x \right)} \tan{\left(x \right)}} 
tan(x)^(1/cos(x))*(cos(x)^2*(1 + tan(x)^2) + cos(x)*log(tan(x))*sin(x)*tan(x))/(cos(x)^3*tan(x))
Respuesta numérica [src] 
tan(x)^(1/cos(x))*((1.0 + tan(x)^2)/(cos(x)*tan(x)) + log(tan(x))*sin(x)/cos(x)^2)
tan(x)^(1/cos(x))*((1.0 + tan(x)^2)/(cos(x)*tan(x)) + log(tan(x))*sin(x)/cos(x)^2)
Combinatoria [src] 
          1                                                         
        ------                                                      
        cos(x) /   2                                               \
(tan(x))      *\tan (x)*cos(x) + log(tan(x))*sin(x)*tan(x) + cos(x)/
--------------------------------------------------------------------
                              2                                     
                           cos (x)*tan(x)
(log⁡(tan⁡(x))sin⁡(x)tan⁡(x)+cos⁡(x)tan⁡2(x)+cos⁡(x))tan⁡1cos⁡(x)(x)cos⁡2(x)tan⁡(x)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \tan{\left(x \right)} + \cos{\left(x \right)} \tan^{2}{\left(x \right)} + \cos{\left(x \right)}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} 
tan(x)^(1/cos(x))*(tan(x)^2*cos(x) + log(tan(x))*sin(x)*tan(x) + cos(x))/(cos(x)^2*tan(x))
Denominador común [src] 
          1                               1                       1                             
        ------                          ------                  ------                          
        cos(x)             2            cos(x)                  cos(x)                          
(tan(x))      *cos(x) + tan (x)*(tan(x))      *cos(x) + (tan(x))      *log(tan(x))*sin(x)*tan(x)
------------------------------------------------------------------------------------------------
                                            2                                                   
                                         cos (x)*tan(x)
log⁡(tan⁡(x))sin⁡(x)tan⁡(x)tan⁡1cos⁡(x)(x)+cos⁡(x)tan⁡2(x)tan⁡1cos⁡(x)(x)+cos⁡(x)tan⁡1cos⁡(x)(x)cos⁡2(x)tan⁡(x)\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \tan{\left(x \right)} \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} + \cos{\left(x \right)} \tan^{2}{\left(x \right)} \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} + \cos{\left(x \right)} \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} 
(tan(x)^(1/cos(x))*cos(x) + tan(x)^2*tan(x)^(1/cos(x))*cos(x) + tan(x)^(1/cos(x))*log(tan(x))*sin(x)*tan(x))/(cos(x)^2*tan(x))
Unión de expresiones racionales [src] 
          1                                                      
        ------                                                   
        cos(x) //       2   \                                   \
(tan(x))      *\\1 + tan (x)/*cos(x) + log(tan(x))*sin(x)*tan(x)/
-----------------------------------------------------------------
                             2                                   
                          cos (x)*tan(x)
((tan⁡2(x)+1)cos⁡(x)+log⁡(tan⁡(x))sin⁡(x)tan⁡(x))tan⁡1cos⁡(x)(x)cos⁡2(x)tan⁡(x)\frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \tan{\left(x \right)}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)} \tan{\left(x \right)}} 
tan(x)^(1/cos(x))*((1 + tan(x)^2)*cos(x) + log(tan(x))*sin(x)*tan(x))/(cos(x)^2*tan(x))
Compilar la expresión [src] 
          1                                        
        ------ /        2                         \
        cos(x) | 1 + tan (x)    log(tan(x))*sin(x)|
(tan(x))      *|------------- + ------------------|
               |cos(x)*tan(x)           2         |
               \                     cos (x)      /
(tan⁡2(x)+1cos⁡(x)tan⁡(x)+log⁡(tan⁡(x))sin⁡(x)cos⁡2(x))tan⁡1cos⁡(x)(x)\left(\frac{\tan^{2}{\left(x \right)} + 1}{\cos{\left(x \right)} \tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
tan(x)^(1/cos(x))*((1 + tan(x)^2)/(cos(x)*tan(x)) + log(tan(x))*sin(x)/cos(x)^2)
Abrimos la expresión [src] 
          1                1                       1                      
        ------           ------                  ------                   
        cos(x)           cos(x)                  cos(x)                   
(tan(x))         (tan(x))      *tan(x)   (tan(x))      *log(tan(x))*sin(x)
-------------- + --------------------- + ---------------------------------
cos(x)*tan(x)            cos(x)                          2                
                                                      cos (x)
log⁡(tan⁡(x))sin⁡(x)tan⁡1cos⁡(x)(x)cos⁡2(x)+tan⁡(x)tan⁡1cos⁡(x)(x)cos⁡(x)+tan⁡1cos⁡(x)(x)cos⁡(x)tan⁡(x)\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)} \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos{\left(x \right)} \tan{\left(x \right)}} 
tan(x)^(1/cos(x))/(cos(x)*tan(x)) + tan(x)^(1/cos(x))*tan(x)/cos(x) + tan(x)^(1/cos(x))*log(tan(x))*sin(x)/cos(x)^2
Potencias [src] 
          1                                        
        ------ /        2                         \
        cos(x) | 1 + tan (x)    log(tan(x))*sin(x)|
(tan(x))      *|------------- + ------------------|
               |cos(x)*tan(x)           2         |
               \                     cos (x)      /
(tan⁡2(x)+1cos⁡(x)tan⁡(x)+log⁡(tan⁡(x))sin⁡(x)cos⁡2(x))tan⁡1cos⁡(x)(x)\left(\frac{\tan^{2}{\left(x \right)} + 1}{\cos{\left(x \right)} \tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                         1                                                                                                
                    ------------ /                                                 /                    2\               \
                     I*x    -I*x |                                                 |    /   I*x    -I*x\ |               |
                    e      e     |                        /  /   I*x    -I*x\\     |    \- e    + e    / | / I*x    -I*x\|
                    ---- + ----- |    /   -I*x    I*x\    |I*\- e    + e    /|   I*|1 - -----------------|*\e    + e    /|
                     2       2   |  I*\- e     + e   /*log|------------------|     |                   2 |               |
/  /   I*x    -I*x\\             |                        |    I*x    -I*x   |     |     / I*x    -I*x\  |               |
|I*\- e    + e    /|             |                        \   e    + e       /     \     \e    + e    /  /               |
|------------------|            *|- ------------------------------------------ - ----------------------------------------|
|    I*x    -I*x   |             |                              2                    / I*x    -I*x\                      |
\   e    + e       /             |                / I*x    -I*x\                     |e      e    | /   I*x    -I*x\     |
                                 |                |e      e    |                     |---- + -----|*\- e    + e    /     |
                                 |              2*|---- + -----|                     \ 2       2  /                      |
                                 \                \ 2       2  /                                                         /
(i(−eix+e−ix)eix+e−ix)1eix2+e−ix2(−i(−(−eix+e−ix)2(eix+e−ix)2+1)(eix+e−ix)(−eix+e−ix)(eix2+e−ix2)−i(eix−e−ix)log⁡(i(−eix+e−ix)eix+e−ix)2(eix2+e−ix2)2)\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}}\right)^{\frac{1}{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}} \left(- \frac{i \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 1\right) \left(e^{i x} + e^{- i x}\right)}{\left(- e^{i x} + e^{- i x}\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)} - \frac{i \left(e^{i x} - e^{- i x}\right) \log{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} \right)}}{2 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}\right) 
(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))^(1/(exp(i*x)/2 + exp(-i*x)/2))*(-i*(-exp(-i*x) + exp(i*x))*log(i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))/(2*(exp(i*x)/2 + exp(-i*x)/2)^2) - i*(1 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(exp(i*x) + exp(-i*x))/((exp(i*x)/2 + exp(-i*x)/2)*(-exp(i*x) + exp(-i*x))))
Parte trigonométrica [src] 
               2/x\                                                                                   
        1 + tan |-|                                                                                   
                \2/                                                                                   
        ----------- /                                                       2              2         \
               2/x\ |                       /x\                /       2/x\\  /       2/x\\          |
        1 - tan |-| |      4*log(tan(x))*tan|-|                |1 + tan |-|| *|1 + tan |-||          |
                \2/ |                       \2/                \        \2//  \        \4//          |
(tan(x))           *|------------------------------- + ----------------------------------------------|
                    |              /           2   \                  2                              |
                    |/       2/x\\ |    1 - tan (x)|     /       2/x\\  /        1   \           2/x\|
                    ||1 + tan |-||*|1 + -----------|   4*|1 - tan |-|| *|-1 + -------|*tan(x)*tan |-||
                    |\        \2// |           2   |     \        \2//  |        2/x\|            \4/|
                    |              \    1 + tan (x)/                    |     tan |-||               |
                    \                                                   \         \2//               /
(4log⁡(tan⁡(x))tan⁡(x2)(1−tan⁡2(x)tan⁡2(x)+1+1)(tan⁡2(x2)+1)+(tan⁡2(x4)+1)2(tan⁡2(x2)+1)24(−1+1tan⁡2(x2))(1−tan⁡2(x2))2tan⁡2(x4)tan⁡(x))tan⁡tan⁡2(x2)+11−tan⁡2(x2)(x)\left(\frac{4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \tan^{2}{\left(\frac{x}{4} \right)} \tan{\left(x \right)}}\right) \tan^{\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}}{\left(x \right)} 
          1    /                                    2/x\                \
        ------ |                                 tan |-|*cot(x)         |
        cos(x) |2*log(tan(x))*sin(x)                 \4/                |
(tan(x))      *|-------------------- + ---------------------------------|
               |    1 + cos(2*x)                       3                |
               |                         /        2/x\\     4/x\    4/x\|
               |                       4*|-1 + cot |-|| *sin |-|*sin |-||
               \                         \         \2//      \2/     \4//
(tan⁡2(x4)cot⁡(x)4(cot⁡2(x2)−1)3sin⁡4(x4)sin⁡4(x2)+2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1)tan⁡1cos⁡(x)(x)\left(\frac{\tan^{2}{\left(\frac{x}{4} \right)} \cot{\left(x \right)}}{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3} \sin^{4}{\left(\frac{x}{4} \right)} \sin^{4}{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
               /                          2       /sec(x)\\
        sec(x) |/       2   \          sec (x)*log|------||
/sec(x)\       ||    sec (x)|                     \csc(x)/|
|------|      *||1 + -------|*csc(x) + -------------------|
\csc(x)/       ||       2   |                 csc(x)      |
               \\    csc (x)/                             /
(sec⁡(x)csc⁡(x))sec⁡(x)((1+sec⁡2(x)csc⁡2(x))csc⁡(x)+log⁡(sec⁡(x)csc⁡(x))sec⁡2(x)csc⁡(x))\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right)^{\sec{\left(x \right)}} \left(\left(1 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)} + \frac{\log{\left(\frac{\sec{\left(x \right)}}{\csc{\left(x \right)}} \right)} \sec^{2}{\left(x \right)}}{\csc{\left(x \right)}}\right) 
          1                                                                       
        ------                                                                    
        cos(x) /log(tan(x))*sin(x)                     sin(2*x)                  \
(tan(x))      *|------------------ + --------------------------------------------|
               |        2            /         4/x\\                             |
               |     cos (x)         |    4*sin |-||                             |
               |                     |          \2/|                 2       2   |
               |                     |1 - ---------|*(1 + cos(x))*cos (x)*sin (x)|
               |                     |        2    |                             |
               \                     \     sin (x) /                             /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+sin⁡(2x)(−4sin⁡4(x2)sin⁡2(x)+1)(cos⁡(x)+1)sin⁡2(x)cos⁡2(x))tan⁡1cos⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\sin{\left(2 x \right)}}{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \left(\cos{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
          1                                                                        
        ------                                                                     
        cos(x) /log(tan(x))*sin(x)                      sin(2*x)                  \
(tan(x))      *|------------------ + ---------------------------------------------|
               |        2                         /         2    \                |
               |     cos (x)                      |      sin (x) |    2       2   |
               |                     (1 - cos(x))*|-1 + ---------|*cos (x)*sin (x)|
               |                                  |          4/x\|                |
               |                                  |     4*sin |-||                |
               \                                  \           \2//                /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+sin⁡(2x)(−1+sin⁡2(x)4sin⁡4(x2))(1−cos⁡(x))sin⁡2(x)cos⁡2(x))tan⁡1cos⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\sin{\left(2 x \right)}}{\left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(1 - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                1                                      
           -----------                                 
              /    pi\                                 
           sin|x + --|                                 
              \    2 /                                 
/     2   \            /            /     2   \       \
|2*sin (x)|            |  1         |2*sin (x)|       |
|---------|           *|------ + log|---------|*sin(x)|
\ sin(2*x)/            \sin(x)      \ sin(2*x)/       /
-------------------------------------------------------
                         2/    pi\                     
                      sin |x + --|                     
                          \    2 /
(2sin⁡2(x)sin⁡(2x))1sin⁡(x+π2)(log⁡(2sin⁡2(x)sin⁡(2x))sin⁡(x)+1sin⁡(x))sin⁡2(x+π2)\frac{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\frac{1}{\sin{\left(x + \frac{\pi}{2} \right)}}} \left(\log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right)}{\sin^{2}{\left(x + \frac{\pi}{2} \right)}} 
          1                                                           
        ------                                                        
        cos(x) /2*log(tan(x))*sin(x)               cot(x)            \
(tan(x))      *|-------------------- + ------------------------------|
               |    1 + cos(2*x)       /        2/x\\    2       2/x\|
               |                       |-1 + cot |-||*cos (x)*sin |-||
               \                       \         \2//             \2//
(cot⁡(x)(cot⁡2(x2)−1)sin⁡2(x2)cos⁡2(x)+2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1)tan⁡1cos⁡(x)(x)\left(\frac{\cot{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
               1                                                
             ------                                             
             cos(x)                                             
/   /    pi\\       /                             /   /    pi\\\
|cos|x - --||       |                             |cos|x - --|||
|   \    2 /|       |     1           /    pi\    |   \    2 /||
|-----------|      *|----------- + cos|x - --|*log|-----------||
\   cos(x)  /       |   /    pi\      \    2 /    \   cos(x)  /|
                    |cos|x - --|                               |
                    \   \    2 /                               /
----------------------------------------------------------------
                               2                                
                            cos (x)
(cos⁡(x−π2)cos⁡(x))1cos⁡(x)(log⁡(cos⁡(x−π2)cos⁡(x))cos⁡(x−π2)+1cos⁡(x−π2))cos⁡2(x)\frac{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)} \cos{\left(x - \frac{\pi}{2} \right)} + \frac{1}{\cos{\left(x - \frac{\pi}{2} \right)}}\right)}{\cos^{2}{\left(x \right)}} 
                              2/x\                                     
                       1 + tan |-|                                     
                               \2/                                     
                       -----------                                     
                              2/x\ /       2/x\                    /x\\
             2         1 - tan |-| |1 + tan |-|   2*log(tan(x))*tan|-||
/       2/x\\                  \2/ |        \2/                    \2/|
|1 + tan |-|| *(tan(x))           *|----------- + --------------------|
\        \2//                      |       /x\               2/x\     |
                                   |  2*tan|-|        1 + tan |-|     |
                                   \       \2/                \2/     /
-----------------------------------------------------------------------
                                          2                            
                             /       2/x\\                             
                             |1 - tan |-||                             
                             \        \2//
(tan⁡2(x2)+12tan⁡(x2)+2log⁡(tan⁡(x))tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x2)+1)2tan⁡tan⁡2(x2)+11−tan⁡2(x2)(x)(1−tan⁡2(x2))2\frac{\left(\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan^{\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}}{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}} 
          1                                                                 
        ------                                                              
        cos(x) /2*log(tan(x))*sin(x)                    1                  \
(tan(x))      *|-------------------- + ------------------------------------|
               |    1 + cos(2*x)       /       2/x\\    2       2/x\       |
               |                       |1 - tan |-||*cos (x)*cos |-|*tan(x)|
               \                       \        \2//             \2/       /
(2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1+1(1−tan⁡2(x2))cos⁡2(x2)cos⁡2(x)tan⁡(x))tan⁡1cos⁡(x)(x)\left(\frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1} + \frac{1}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \cos^{2}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)} \tan{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                    /         /   sec(x)  \                                      \
                    |    2*log|-----------|                                      |
                    |         |   /    pi\|          2/x   pi\           /    pi\|
             sec(x) |         |sec|x - --||       sec |- - --|*sec(x)*sec|x - --||
/   sec(x)  \       |         \   \    2 //           \2   2 /           \    2 /|
|-----------|      *|-------------------------- + -------------------------------|
|   /    pi\|       |/       1    \    /    pi\                  2/x   pi\       |
|sec|x - --||       ||1 + --------|*sec|x - --|               sec |- - --|       |
\   \    2 //       |\    sec(2*x)/    \    2 /                   \2   2 /       |
                    |                                    -1 + ------------       |
                    |                                              2/x\          |
                    |                                           sec |-|          |
                    \                                               \2/          /
(sec⁡(x)sec⁡(x−π2))sec⁡(x)(2log⁡(sec⁡(x)sec⁡(x−π2))(1+1sec⁡(2x))sec⁡(x−π2)+sec⁡(x)sec⁡2(x2−π2)sec⁡(x−π2)−1+sec⁡2(x2−π2)sec⁡2(x2))\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sec{\left(x \right)}} \left(\frac{2 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{\sec{\left(x \right)} \sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \frac{\pi}{2} \right)}}{-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}}\right) 
               2/x\                                                     
        1 + cot |-|                                                     
                \2/                                                     
        ------------                                                    
                2/x\                                                    
        -1 + cot |-|                /       2/x\        /x\    /  1   \\
                 \2/              2 |1 + cot |-|   2*cot|-|*log|------||
/  1   \             /       2/x\\  |        \2/        \2/    \cot(x)/|
|------|            *|1 + cot |-|| *|----------- + --------------------|
\cot(x)/             \        \2//  |       /x\               2/x\     |
                                    |  2*cot|-|        1 + cot |-|     |
                                    \       \2/                \2/     /
------------------------------------------------------------------------
                                          2                             
                            /        2/x\\                              
                            |-1 + cot |-||                              
                            \         \2//
(cot⁡2(x2)+12cot⁡(x2)+2log⁡(1cot⁡(x))cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x2)+1)2(1cot⁡(x))cot⁡2(x2)+1cot⁡2(x2)−1(cot⁡2(x2)−1)2\frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)} \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \left(\frac{1}{\cot{\left(x \right)}}\right)^{\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} \right)} - 1}}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}} 
                            /   /   sec(x)  \              \
                            |log|-----------|              |
                            |   |   /    pi\|              |
             sec(x)         |   |sec|x - --||              |
/   sec(x)  \          2    |   \   \    2 //      /    pi\|
|-----------|      *sec (x)*|---------------- + sec|x - --||
|   /    pi\|               |     /    pi\         \    2 /|
|sec|x - --||               |  sec|x - --|                 |
\   \    2 //               \     \    2 /                 /
(sec⁡(x)sec⁡(x−π2))sec⁡(x)(log⁡(sec⁡(x)sec⁡(x−π2))sec⁡(x−π2)+sec⁡(x−π2))sec⁡2(x)\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sec{\left(x \right)}} \left(\frac{\log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} + \sec{\left(x - \frac{\pi}{2} \right)}\right) \sec^{2}{\left(x \right)} 
   sec(x)    /  1                        \
tan      (x)*|------ + log(tan(x))*sin(x)|
             \sin(x)                     /
------------------------------------------
                    2                     
                 cos (x)
(log⁡(tan⁡(x))sin⁡(x)+1sin⁡(x))tan⁡sec⁡(x)(x)cos⁡2(x)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right) \tan^{\sec{\left(x \right)}}{\left(x \right)}}{\cos^{2}{\left(x \right)}} 
               2/x\                                                                                    
        1 + cot |-|                                                                                    
                \2/                                                                                    
        ------------                                                                                   
                2/x\ /                                                     2              2           \
        -1 + cot |-| |           /x\    /  1   \              /       2/x\\  /       2/x\\            |
                 \2/ |      4*cot|-|*log|------|              |1 + cot |-|| *|1 + cot |-|| *cot(x)    |
/  1   \             |           \2/    \cot(x)/              \        \2//  \        \4//            |
|------|            *|-------------------------------- + ---------------------------------------------|
\cot(x)/             |              /            2   \                               2               2|
                     |/       2/x\\ |    -1 + cot (x)|   /       1   \ /        2/x\\  /        2/x\\ |
                     ||1 + cot |-||*|1 + ------------|   |1 - -------|*|-1 + cot |-|| *|-1 + cot |-|| |
                     |\        \2// |           2    |   |       2/x\| \         \2//  \         \4// |
                     |              \    1 + cot (x) /   |    cot |-||                                |
                     \                                   \        \2//                                /
(4log⁡(1cot⁡(x))cot⁡(x2)(cot⁡2(x)−1cot⁡2(x)+1+1)(cot⁡2(x2)+1)+(cot⁡2(x4)+1)2(cot⁡2(x2)+1)2cot⁡(x)(1−1cot⁡2(x2))(cot⁡2(x4)−1)2(cot⁡2(x2)−1)2)(1cot⁡(x))cot⁡2(x2)+1cot⁡2(x2)−1\left(\frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} \right)} - 1}} 
               /       2                        \
          1    |    sin (x)                     |
        ------ |1 + -------      /sin(x)\       |
        cos(x) |       2      log|------|*sin(x)|
/sin(x)\       |    cos (x)      \cos(x)/       |
|------|      *|----------- + ------------------|
\cos(x)/       |   sin(x)             2         |
               \                   cos (x)      /
(sin⁡(x)cos⁡(x))1cos⁡(x)(sin⁡2(x)cos⁡2(x)+1sin⁡(x)+log⁡(sin⁡(x)cos⁡(x))sin⁡(x)cos⁡2(x))\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\frac{\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1}{\sin{\left(x \right)}} + \frac{\log{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) 
          1                                                                        
        ------                                                                     
        cos(x) /2*log(tan(x))*sin(x)                  2*(1 - cos(x))              \
(tan(x))      *|-------------------- + -------------------------------------------|
               |    1 + cos(2*x)                   2              2               |
               |                       /       /x\\  /        /x\\     /x\    3   |
               |                       |1 + tan|-|| *|-1 + tan|-|| *cos|-|*sin (x)|
               \                       \       \2//  \        \2//     \2/        /
(2(1−cos⁡(x))(tan⁡(x2)−1)2(tan⁡(x2)+1)2sin⁡3(x)cos⁡(x2)+2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1)tan⁡1cos⁡(x)(x)\left(\frac{2 \left(1 - \cos{\left(x \right)}\right)}{\left(\tan{\left(\frac{x}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{x}{2} \right)} + 1\right)^{2} \sin^{3}{\left(x \right)} \cos{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
               1                                                                                    
             ------ /                 /   /    pi\\                                                \
             cos(x) |                 |cos|x - --||                                                |
/   /    pi\\       |     /    pi\    |   \    2 /|                                                |
|cos|x - --||       |2*cos|x - --|*log|-----------|                                                |
|   \    2 /|       |     \    2 /    \   cos(x)  /                         1                      |
|-----------|      *|------------------------------ + ---------------------------------------------|
\   cos(x)  /       |         1 + cos(2*x)            /       2/x   pi\\                           |
                    |                                 |    cos |- - --||                           |
                    |                                 |        \2   2 /|           2/x\    /    pi\|
                    |                                 |1 - ------------|*cos(x)*cos |-|*cos|x - --||
                    |                                 |         2/x\   |            \2/    \    2 /|
                    |                                 |      cos |-|   |                           |
                    \                                 \          \2/   /                           /
(cos⁡(x−π2)cos⁡(x))1cos⁡(x)(2log⁡(cos⁡(x−π2)cos⁡(x))cos⁡(x−π2)cos⁡(2x)+1+1(1−cos⁡2(x2−π2)cos⁡2(x2))cos⁡2(x2)cos⁡(x)cos⁡(x−π2))\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\frac{2 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} + 1} + \frac{1}{\left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos^{2}{\left(\frac{x}{2} \right)} \cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}\right) 
                /pi    \                                         
             csc|-- - x|              /   /   /pi    \\         \
                \2     /              |   |csc|-- - x||         |
/   /pi    \\                         |   |   \2     /|         |
|csc|-- - x||                         |log|-----------|         |
|   \2     /|               2/pi    \ |   \   csc(x)  /         |
|-----------|           *csc |-- - x|*|---------------- + csc(x)|
\   csc(x)  /                \2     / \     csc(x)              /
(csc⁡(−x+π2)csc⁡(x))csc⁡(−x+π2)(log⁡(csc⁡(−x+π2)csc⁡(x))csc⁡(x)+csc⁡(x))csc⁡2(−x+π2)\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\csc{\left(- x + \frac{\pi}{2} \right)}} \left(\frac{\log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{\csc{\left(x \right)}} + \csc{\left(x \right)}\right) \csc^{2}{\left(- x + \frac{\pi}{2} \right)} 
               2/x\                                                                   
        1 + tan |-|                                                                   
                \2/                                                                   
        -----------                                                                   
               2/x\ //       2   \ /       2/x\\     /       2/x\\                /x\\
        1 - tan |-| |\1 + tan (x)/*|1 + tan |-||   2*|1 + tan |-||*log(tan(x))*tan|-||
                \2/ |              \        \2//     \        \2//                \2/|
(tan(x))           *|--------------------------- + ----------------------------------|
                    |    /       2/x\\                                    2          |
                    |    |1 - tan |-||*tan(x)                /       2/x\\           |
                    |    \        \2//                       |1 - tan |-||           |
                    \                                        \        \2//           /
((tan⁡2(x2)+1)(tan⁡2(x)+1)(1−tan⁡2(x2))tan⁡(x)+2(tan⁡2(x2)+1)log⁡(tan⁡(x))tan⁡(x2)(1−tan⁡2(x2))2)tan⁡tan⁡2(x2)+11−tan⁡2(x2)(x)\left(\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}\right) \tan^{\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}}{\left(x \right)} 
               2/x\                                                                         
        1 + tan |-|                                                                         
                \2/                                                                         
        ----------- /                                                  2              2    \
               2/x\ |                       /x\           /       2/x\\  /       2/x\\     |
        1 - tan |-| |      4*log(tan(x))*tan|-|           |1 + tan |-|| *|1 + tan |-||     |
                \2/ |                       \2/           \        \2//  \        \4//     |
(tan(x))           *|------------------------------- + ------------------------------------|
                    |              /           2   \                3              2       |
                    |/       2/x\\ |    1 - tan (x)|   /       2/x\\  /       2/x\\        |
                    ||1 + tan |-||*|1 + -----------|   |1 - tan |-|| *|1 - tan |-|| *tan(x)|
                    |\        \2// |           2   |   \        \2//  \        \4//        |
                    \              \    1 + tan (x)/                                       /
(4log⁡(tan⁡(x))tan⁡(x2)(1−tan⁡2(x)tan⁡2(x)+1+1)(tan⁡2(x2)+1)+(tan⁡2(x4)+1)2(tan⁡2(x2)+1)2(1−tan⁡2(x4))2(1−tan⁡2(x2))3tan⁡(x))tan⁡tan⁡2(x2)+11−tan⁡2(x2)(x)\left(\frac{4 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3} \tan{\left(x \right)}}\right) \tan^{\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{1 - \tan^{2}{\left(\frac{x}{2} \right)}}}{\left(x \right)} 
                    /         /   sec(x)  \                                 \
                    |    2*log|-----------|                                 |
                    |         |   /    pi\|          2/x\           /    pi\|
             sec(x) |         |sec|x - --||       sec |-|*sec(x)*sec|x - --||
/   sec(x)  \       |         \   \    2 //           \2/           \    2 /|
|-----------|      *|-------------------------- + --------------------------|
|   /    pi\|       |/       1    \    /    pi\                 2/x\        |
|sec|x - --||       ||1 + --------|*sec|x - --|              sec |-|        |
\   \    2 //       |\    sec(2*x)/    \    2 /                  \2/        |
                    |                                  1 - ------------     |
                    |                                         2/x   pi\     |
                    |                                      sec |- - --|     |
                    \                                          \2   2 /     /
(sec⁡(x)sec⁡(x−π2))sec⁡(x)(sec⁡2(x2)sec⁡(x)sec⁡(x−π2)−sec⁡2(x2)sec⁡2(x2−π2)+1+2log⁡(sec⁡(x)sec⁡(x−π2))(1+1sec⁡(2x))sec⁡(x−π2))\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sec{\left(x \right)}} \left(\frac{\sec^{2}{\left(\frac{x}{2} \right)} \sec{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}}{- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1} + \frac{2 \log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}\right) 
               2/x\                                                                           
        1 + cot |-|                                                                           
                \2/                                                                           
        ------------                                                                          
                2/x\ //       1   \ /       2/x\\                                            \
        -1 + cot |-| ||1 + -------|*|1 + cot |-||*cot(x)     /       2/x\\    /x\    /  1   \|
                 \2/ ||       2   | \        \2//          2*|1 + cot |-||*cot|-|*log|------||
/  1   \             |\    cot (x)/                          \        \2//    \2/    \cot(x)/|
|------|            *|---------------------------------- + ----------------------------------|
\cot(x)/             |                   2/x\                                     2          |
                     |           -1 + cot |-|                       /        2/x\\           |
                     |                    \2/                       |-1 + cot |-||           |
                     \                                              \         \2//           /
((1+1cot⁡2(x))(cot⁡2(x2)+1)cot⁡(x)cot⁡2(x2)−1+2(cot⁡2(x2)+1)log⁡(1cot⁡(x))cot⁡(x2)(cot⁡2(x2)−1)2)(1cot⁡(x))cot⁡2(x2)+1cot⁡2(x2)−1\left(\frac{\left(1 + \frac{1}{\cot^{2}{\left(x \right)}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\frac{1}{\cot{\left(x \right)}} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} \right)} - 1}} 
   sec(x)    /        4           log(tan(x))*sin(x)\
tan      (x)*|----------------- + ------------------|
             |sin(x) + sin(3*x)           2         |
             \                         cos (x)      /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+4sin⁡(x)+sin⁡(3x))tan⁡sec⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{4}{\sin{\left(x \right)} + \sin{\left(3 x \right)}}\right) \tan^{\sec{\left(x \right)}}{\left(x \right)} 
          1                                 
        ------                              
        cos(x) /  1                        \
(tan(x))      *|------ + log(tan(x))*sin(x)|
               \sin(x)                     /
--------------------------------------------
                        2                   
          /        2/x\\     4/x\           
          |-1 + cot |-|| *sin |-|           
          \         \2//      \2/
(log⁡(tan⁡(x))sin⁡(x)+1sin⁡(x))tan⁡1cos⁡(x)(x)(cot⁡2(x2)−1)2sin⁡4(x2)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}} 
             /                           2/x\          \
             |                        sec |-|*sec(x)   |
   sec(x)    |log(tan(x))*sin(x)          \2/          |
tan      (x)*|------------------ + --------------------|
             |        2            /       2/x\\       |
             |     cos (x)         |1 - tan |-||*sin(x)|
             \                     \        \2//       /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+sec⁡2(x2)sec⁡(x)(1−tan⁡2(x2))sin⁡(x))tan⁡sec⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{\sec^{2}{\left(\frac{x}{2} \right)} \sec{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \sin{\left(x \right)}}\right) \tan^{\sec{\left(x \right)}}{\left(x \right)} 
   2       sec(x)    /  1                        \
sec (x)*tan      (x)*|------ + log(tan(x))*sin(x)|
                     \sin(x)                     /
(log⁡(tan⁡(x))sin⁡(x)+1sin⁡(x))tan⁡sec⁡(x)(x)sec⁡2(x)\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right) \tan^{\sec{\left(x \right)}}{\left(x \right)} \sec^{2}{\left(x \right)} 
          1                                 
        ------                              
        cos(x)                              
(tan(x))      *(log(tan(x))*sin(x) + csc(x))
--------------------------------------------
                     2                      
                  cos (x)
(log⁡(tan⁡(x))sin⁡(x)+csc⁡(x))tan⁡1cos⁡(x)(x)cos⁡2(x)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \csc{\left(x \right)}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)}} 
          1                                                                                          
        ------                                                                                       
        cos(x) /2*log(tan(x))*sin(x)                               cot(x)                           \
(tan(x))      *|-------------------- + -------------------------------------------------------------|
               |    1 + cos(2*x)                                   2               2                |
               |                       /       2/x\\ /        2/x\\  /        2/x\\     4/x\    4/x\|
               |                       |1 - tan |-||*|-1 + cot |-|| *|-1 + cot |-|| *sin |-|*sin |-||
               \                       \        \2// \         \2//  \         \4//      \2/     \4//
(2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1+cot⁡(x)(1−tan⁡2(x2))(cot⁡2(x4)−1)2(cot⁡2(x2)−1)2sin⁡4(x4)sin⁡4(x2))tan⁡1cos⁡(x)(x)\left(\frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1} + \frac{\cot{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)} \sin^{4}{\left(\frac{x}{2} \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                /pi    \                                                          
             csc|-- - x| /         /   /pi    \\                                 \
                \2     / |         |csc|-- - x||                                 |
/   /pi    \\            |         |   \2     /|          2/x\           /pi    \|
|csc|-- - x||            |    2*log|-----------|       csc |-|*csc(x)*csc|-- - x||
|   \2     /|            |         \   csc(x)  /           \2/           \2     /|
|-----------|           *|-------------------------- + --------------------------|
\   csc(x)  /            |/          1      \                        2/x\        |
                         ||1 + -------------|*csc(x)              csc |-|        |
                         ||       /pi      \|                         \2/        |
                         ||    csc|-- - 2*x||              -1 + ------------     |
                         |\       \2       //                      2/pi   x\     |
                         |                                      csc |-- - -|     |
                         \                                          \2    2/     /
(csc⁡(−x+π2)csc⁡(x))csc⁡(−x+π2)(csc⁡2(x2)csc⁡(x)csc⁡(−x+π2)csc⁡2(x2)csc⁡2(−x2+π2)−1+2log⁡(csc⁡(−x+π2)csc⁡(x))(1+1csc⁡(−2x+π2))csc⁡(x))\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\csc{\left(- x + \frac{\pi}{2} \right)}} \left(\frac{\csc^{2}{\left(\frac{x}{2} \right)} \csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1} + \frac{2 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{\left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}\right) 
               1    /       2/    pi\                               \
             ------ |    cos |x - --|                  /   /    pi\\|
             cos(x) |        \    2 /                  |cos|x - --|||
/   /    pi\\       |1 + ------------      /    pi\    |   \    2 /||
|cos|x - --||       |         2         cos|x - --|*log|-----------||
|   \    2 /|       |      cos (x)         \    2 /    \   cos(x)  /|
|-----------|      *|---------------- + ----------------------------|
\   cos(x)  /       |     /    pi\                   2              |
                    |  cos|x - --|                cos (x)           |
                    \     \    2 /                                  /
(cos⁡(x−π2)cos⁡(x))1cos⁡(x)(1+cos⁡2(x−π2)cos⁡2(x)cos⁡(x−π2)+log⁡(cos⁡(x−π2)cos⁡(x))cos⁡(x−π2)cos⁡2(x))\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\frac{1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) 
               1                                                                                          
             ------ /                 /   /    pi\\                                                      \
             cos(x) |                 |cos|x - --||                                                      |
/   /    pi\\       |     /    pi\    |   \    2 /|                                                      |
|cos|x - --||       |2*cos|x - --|*log|-----------|                                                      |
|   \    2 /|       |     \    2 /    \   cos(x)  /                            1                         |
|-----------|      *|------------------------------ + ---------------------------------------------------|
\   cos(x)  /       |         1 + cos(2*x)            /          2/x\   \                                |
                    |                                 |       cos |-|   |                                |
                    |                                 |           \2/   |           /    pi\    2/x   pi\|
                    |                                 |-1 + ------------|*cos(x)*cos|x - --|*cos |- - --||
                    |                                 |        2/x   pi\|           \    2 /     \2   2 /|
                    |                                 |     cos |- - --||                                |
                    \                                 \         \2   2 //                                /
(cos⁡(x−π2)cos⁡(x))1cos⁡(x)(2log⁡(cos⁡(x−π2)cos⁡(x))cos⁡(x−π2)cos⁡(2x)+1+1(cos⁡2(x2)cos⁡2(x2−π2)−1)cos⁡(x)cos⁡2(x2−π2)cos⁡(x−π2))\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\frac{2 \log{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} + 1} + \frac{1}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right) \cos{\left(x \right)} \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \cos{\left(x - \frac{\pi}{2} \right)}}\right) 
                1                                                                                     
           -----------                                                                                
              /    pi\                                                                                
           sin|x + --| /     /     2   \                                                             \
              \    2 / |     |2*sin (x)|                                                             |
/     2   \            |2*log|---------|*sin(x)                                                      |
|2*sin (x)|            |     \ sin(2*x)/                                sin(2*x)                     |
|---------|           *|----------------------- + ---------------------------------------------------|
\ sin(2*x)/            |          /pi      \        /         4/x\\                                  |
                       |   1 + sin|-- + 2*x|        |    4*sin |-||                                  |
                       |          \2       /        |          \2/|    2       2/    pi\    2/pi   x\|
                       |                          2*|1 - ---------|*sin (x)*sin |x + --|*sin |-- + -||
                       |                            |        2    |             \    2 /     \2    2/|
                       \                            \     sin (x) /                                  /
(2sin⁡2(x)sin⁡(2x))1sin⁡(x+π2)(2log⁡(2sin⁡2(x)sin⁡(2x))sin⁡(x)sin⁡(2x+π2)+1+sin⁡(2x)2(−4sin⁡4(x2)sin⁡2(x)+1)sin⁡2(x)sin⁡2(x2+π2)sin⁡2(x+π2))\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\frac{1}{\sin{\left(x + \frac{\pi}{2} \right)}}} \left(\frac{2 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)} \sin{\left(x \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin^{2}{\left(x \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)} \sin^{2}{\left(x + \frac{\pi}{2} \right)}}\right) 
               2/x\                                                                           
        1 + cot |-|                                                                           
                \2/                                                                           
        ------------                                                                          
                2/x\ /                                                2              2       \
        -1 + cot |-| |           /x\    /  1   \         /       2/x\\  /       2/x\\        |
                 \2/ |      4*cot|-|*log|------|         |1 + cot |-|| *|1 + cot |-|| *cot(x)|
/  1   \             |           \2/    \cot(x)/         \        \2//  \        \4//        |
|------|            *|-------------------------------- + ------------------------------------|
\cot(x)/             |              /            2   \                        3              |
                     |/       2/x\\ |    -1 + cot (x)|          /        2/x\\     2/x\      |
                     ||1 + cot |-||*|1 + ------------|        4*|-1 + cot |-|| *cot |-|      |
                     |\        \2// |           2    |          \         \2//      \4/      |
                     \              \    1 + cot (x) /                                       /
((cot⁡2(x4)+1)2(cot⁡2(x2)+1)2cot⁡(x)4(cot⁡2(x2)−1)3cot⁡2(x4)+4log⁡(1cot⁡(x))cot⁡(x2)(cot⁡2(x)−1cot⁡2(x)+1+1)(cot⁡2(x2)+1))(1cot⁡(x))cot⁡2(x2)+1cot⁡2(x2)−1\left(\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(x \right)}}{4 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3} \cot^{2}{\left(\frac{x}{4} \right)}} + \frac{4 \log{\left(\frac{1}{\cot{\left(x \right)}} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}\right) \left(\frac{1}{\cot{\left(x \right)}}\right)^{\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} \right)} - 1}} 
                /pi    \                                                            
             csc|-- - x| /                                            /   /pi    \\\
                \2     / |                                            |csc|-- - x|||
/   /pi    \\            |/       2/pi    \\             2/pi    \    |   \2     /||
|csc|-- - x||            ||    csc |-- - x||          csc |-- - x|*log|-----------||
|   \2     /|            ||        \2     /|              \2     /    \   csc(x)  /|
|-----------|           *||1 + ------------|*csc(x) + -----------------------------|
\   csc(x)  /            ||         2      |                      csc(x)           |
                         \\      csc (x)   /                                       /
(csc⁡(−x+π2)csc⁡(x))csc⁡(−x+π2)((1+csc⁡2(−x+π2)csc⁡2(x))csc⁡(x)+log⁡(csc⁡(−x+π2)csc⁡(x))csc⁡2(−x+π2)csc⁡(x))\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\csc{\left(- x + \frac{\pi}{2} \right)}} \left(\left(1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)} + \frac{\log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right) 
                    /                                    2       /   sec(x)  \\
                    |                                 sec (x)*log|-----------||
                    |                                            |   /    pi\||
             sec(x) |/         2      \                          |sec|x - --|||
/   sec(x)  \       ||      sec (x)   |    /    pi\              \   \    2 //|
|-----------|      *||1 + ------------|*sec|x - --| + ------------------------|
|   /    pi\|       ||       2/    pi\|    \    2 /            /    pi\       |
|sec|x - --||       ||    sec |x - --||                     sec|x - --|       |
\   \    2 //       \\        \    2 //                        \    2 /       /
(sec⁡(x)sec⁡(x−π2))sec⁡(x)((sec⁡2(x)sec⁡2(x−π2)+1)sec⁡(x−π2)+log⁡(sec⁡(x)sec⁡(x−π2))sec⁡2(x)sec⁡(x−π2))\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)^{\sec{\left(x \right)}} \left(\left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)} + \frac{\log{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)} \sec^{2}{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) 
          1                                 
        ------                              
        cos(x) /  1                        \
(tan(x))      *|------ + log(tan(x))*sin(x)|
               \sin(x)                     /
--------------------------------------------
                        2                   
           /       2/x\\     4/x\           
           |1 - tan |-|| *cos |-|           
           \        \2//      \2/
(log⁡(tan⁡(x))sin⁡(x)+1sin⁡(x))tan⁡1cos⁡(x)(x)(1−tan⁡2(x2))2cos⁡4(x2)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \cos^{4}{\left(\frac{x}{2} \right)}} 
          1                                            
        ------                                         
        cos(x) /        4           log(tan(x))*sin(x)\
(tan(x))      *|----------------- + ------------------|
               |sin(x) + sin(3*x)           2         |
               \                         cos (x)      /
(log⁡(tan⁡(x))sin⁡(x)cos⁡2(x)+4sin⁡(x)+sin⁡(3x))tan⁡1cos⁡(x)(x)\left(\frac{\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{4}{\sin{\left(x \right)} + \sin{\left(3 x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                1                                                        
           -----------                                                   
              /    pi\ /                        /         4   \         \
           sin|x + --| |   /     2   \          |    4*sin (x)|         |
              \    2 / |   |2*sin (x)|          |1 + ---------|*sin(2*x)|
/     2   \            |log|---------|*sin(x)   |       2     |         |
|2*sin (x)|            |   \ sin(2*x)/          \    sin (2*x)/         |
|---------|           *|--------------------- + ------------------------|
\ sin(2*x)/            |        2/    pi\             2       /    pi\  |
                       |     sin |x + --|        2*sin (x)*sin|x + --|  |
                       \         \    2 /                     \    2 /  /
(2sin⁡2(x)sin⁡(2x))1sin⁡(x+π2)((4sin⁡4(x)sin⁡2(2x)+1)sin⁡(2x)2sin⁡2(x)sin⁡(x+π2)+log⁡(2sin⁡2(x)sin⁡(2x))sin⁡(x)sin⁡2(x+π2))\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\frac{1}{\sin{\left(x + \frac{\pi}{2} \right)}}} \left(\frac{\left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}} + \frac{\log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)} \sin{\left(x \right)}}{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}\right) 
          1                                                                                 
        ------                                                                              
        cos(x) /2*log(tan(x))*sin(x)                            1                          \
(tan(x))      *|-------------------- + ----------------------------------------------------|
               |    1 + cos(2*x)                    3              2                       |
               |                       /       2/x\\  /       2/x\\     4/x\    4/x\       |
               |                       |1 - tan |-|| *|1 - tan |-|| *cos |-|*cos |-|*tan(x)|
               \                       \        \2//  \        \4//      \2/     \4/       /
(2log⁡(tan⁡(x))sin⁡(x)cos⁡(2x)+1+1(1−tan⁡2(x4))2(1−tan⁡2(x2))3cos⁡4(x4)cos⁡4(x2)tan⁡(x))tan⁡1cos⁡(x)(x)\left(\frac{2 \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}}{\cos{\left(2 x \right)} + 1} + \frac{1}{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3} \cos^{4}{\left(\frac{x}{4} \right)} \cos^{4}{\left(\frac{x}{2} \right)} \tan{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)} 
                /pi    \                                                               
             csc|-- - x| /         /   /pi    \\                                      \
                \2     / |         |csc|-- - x||                                      |
/   /pi    \\            |         |   \2     /|          2/pi   x\           /pi    \|
|csc|-- - x||            |    2*log|-----------|       csc |-- - -|*csc(x)*csc|-- - x||
|   \2     /|            |         \   csc(x)  /           \2    2/           \2     /|
|-----------|           *|-------------------------- + -------------------------------|
\   csc(x)  /            |/          1      \                         2/pi   x\       |
                         ||1 + -------------|*csc(x)               csc |-- - -|       |
                         ||       /pi      \|                          \2    2/       |
                         ||    csc|-- - 2*x||                  1 - ------------       |
                         |\       \2       //                           2/x\          |
                         |                                           csc |-|          |
                         \                                               \2/          /
(csc⁡(−x+π2)csc⁡(x))csc⁡(−x+π2)(2log⁡(csc⁡(−x+π2)csc⁡(x))(1+1csc⁡(−2x+π2))csc⁡(x)+csc⁡(x)csc⁡(−x+π2)csc⁡2(−x2+π2)1−csc⁡2(−x2+π2)csc⁡2(x2))\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{\csc{\left(- x + \frac{\pi}{2} \right)}} \left(\frac{2 \log{\left(\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} \right)}}{\left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}} + \frac{\csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)} \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}}\right) 
             1    /                        /         4   \         \
           ------ |   /     2   \          |    4*sin (x)|         |
           cos(x) |   |2*sin (x)|          |1 + ---------|*sin(2*x)|
/     2   \       |log|---------|*sin(x)   |       2     |         |
|2*sin (x)|       |   \ sin(2*x)/          \    sin (2*x)/         |
|---------|      *|--------------------- + ------------------------|
\ sin(2*x)/       |          2                             2       |
                  \       cos (x)              2*cos(x)*sin (x)    /
(2sin⁡2(x)sin⁡(2x))1cos⁡(x)((4sin⁡4(x)sin⁡2(2x)+1)sin⁡(2x)2sin⁡2(x)cos⁡(x)+log⁡(2sin⁡2(x)sin⁡(2x))sin⁡(x)cos⁡2(x))\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\frac{1}{\cos{\left(x \right)}}} \left(\frac{\left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right) \sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}} + \frac{\log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)} \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) 
          1                                 
        ------                              
        cos(x) /  1                        \
(tan(x))      *|------ + log(tan(x))*sin(x)|
               \sin(x)                     /
--------------------------------------------
                     2                      
                  cos (x)
(log⁡(tan⁡(x))sin⁡(x)+1sin⁡(x))tan⁡1cos⁡(x)(x)cos⁡2(x)\frac{\left(\log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{1}{\sin{\left(x \right)}}\right) \tan^{\frac{1}{\cos{\left(x \right)}}}{\left(x \right)}}{\cos^{2}{\left(x \right)}} 
                1                                                                                 
           -----------                                                                            
              /    pi\                                                                            
           sin|x + --| /     /     2   \                                                         \
              \    2 / |     |2*sin (x)|                                                         |
/     2   \            |2*log|---------|*sin(x)                                                  |
|2*sin (x)|            |     \ sin(2*x)/                              sin(2*x)                   |
|---------|           *|----------------------- + -----------------------------------------------|
\ sin(2*x)/            |          /pi      \        /         2    \                             |
                       |   1 + sin|-- + 2*x|        |      sin (x) |    2       2/x\    2/    pi\|
                       |          \2       /      2*|-1 + ---------|*sin (x)*sin |-|*sin |x + --||
                       |                            |          4/x\|             \2/     \    2 /|
                       |                            |     4*sin |-||                             |
                       \                            \           \2//                             /
(2sin⁡2(x)sin⁡(2x))1sin⁡(x+π2)(2log⁡(2sin⁡2(x)sin⁡(2x))sin⁡(x)sin⁡(2x+π2)+1+sin⁡(2x)2(−1+sin⁡2(x)4sin⁡4(x2))sin⁡2(x2)sin⁡2(x)sin⁡2(x+π2))\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right)^{\frac{1}{\sin{\left(x + \frac{\pi}{2} \right)}}} \left(\frac{2 \log{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} \right)} \sin{\left(x \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1} + \frac{\sin{\left(2 x \right)}}{2 \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin^{2}{\left(x \right)} \sin^{2}{\left(x + \frac{\pi}{2} \right)}}\right) 
(2*sin(x)^2/sin(2*x))^(1/sin(x + pi/2))*(2*log(2*sin(x)^2/sin(2*x))*sin(x)/(1 + sin(pi/2 + 2*x)) + sin(2*x)/(2*(-1 + sin(x)^2/(4*sin(x/2)^4))*sin(x)^2*sin(x/2)^2*sin(x + pi/2)^2))
    © Sr Examen – Калькулятор