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Simplificación de expresiones/ Descomposición en fracciones simples/ log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2)-log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)-2*tan(x/2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)+2*tan(x/2)^3/(4+4*tan(x/2)^4+8*tan(x/2)^2)+4*tan(x/2)^2/(4+4*tan(x/2)^4+8*tan(x/2)^2)+tan(x/2)^4*log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2)-tan(x/2)^4*log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)-2*tan(x/2)^2*log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)+2*tan(x/2)^2*log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2)

¿Cómo vas a descomponer esta log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2)-log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)-2*tan(x/2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)+2*tan(x/2)^3/(4+4*tan(x/2)^4+8*tan(x/2)^2)+4*tan(x/2)^2/(4+4*tan(x/2)^4+8*tan(x/2)^2)+tan(x/2)^4*log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2)-tan(x/2)^4*log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)-2*tan(x/2)^2*log(1+tan(x/2)^2)/(4+4*tan(x/2)^4+8*tan(x/2)^2)+2*tan(x/2)^2*log(1-tan(x/2)^2+2*tan(x/2))/(4+4*tan(x/2)^4+8*tan(x/2)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /       2/x\        /x\\           /       2/x\\                     /x\                        3/x\                        2/x\              4/x\    /       2/x\        /x\\       4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\
log|1 - tan |-| + 2*tan|-||        log|1 + tan |-||                2*tan|-|                   2*tan |-|                   4*tan |-|           tan |-|*log|1 - tan |-| + 2*tan|-||    tan |-|*log|1 + tan |-||   2*tan |-|*log|1 + tan |-||   2*tan |-|*log|1 - tan |-| + 2*tan|-||
   \        \2/        \2//           \        \2//                     \2/                         \2/                         \2/               \2/    \        \2/        \2//        \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//
--------------------------- - ------------------------- - ------------------------- + ------------------------- + ------------------------- + ----------------------------------- - ------------------------- - -------------------------- + -------------------------------------
          4/x\        2/x\             4/x\        2/x\            4/x\        2/x\            4/x\        2/x\            4/x\        2/x\                 4/x\        2/x\                 4/x\        2/x\            4/x\        2/x\                   4/x\        2/x\      
 4 + 4*tan |-| + 8*tan |-|    4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|          4 + 4*tan |-| + 8*tan |-|      
           \2/         \2/              \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/                  \2/         \2/                  \2/         \2/             \2/         \2/                    \2/         \2/
log⁡((1−tan⁡2(x2))+2tan⁡(x2))2tan⁡2(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2)+(−log⁡(tan⁡2(x2)+1)2tan⁡2(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2)+(−log⁡(tan⁡2(x2)+1)tan⁡4(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2)+(log⁡((1−tan⁡2(x2))+2tan⁡(x2))tan⁡4(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2)+((((log⁡((1−tan⁡2(x2))+2tan⁡(x2))(4tan⁡4(x2)+4)+8tan⁡2(x2)−log⁡(tan⁡2(x2)+1)(4tan⁡4(x2)+4)+8tan⁡2(x2))−2tan⁡(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2))+2tan⁡3(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2))+4tan⁡2(x2)(4tan⁡4(x2)+4)+8tan⁡2(x2)))))\frac{\log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)} 2 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}} + \left(- \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} 2 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}} + \left(- \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}} + \left(\frac{\log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}} + \left(\left(\left(\left(\frac{\log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}}\right) - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}}\right) + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}}\right) + \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(4 \tan^{4}{\left(\frac{x}{2} \right)} + 4\right) + 8 \tan^{2}{\left(\frac{x}{2} \right)}}\right)\right)\right)\right) 
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + (2*tan(x/2)^3)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + (4*tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + (tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2)))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - (2*tan(x/2)^2)*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + ((2*tan(x/2)^2)*log(1 - tan(x/2)^2 + 2*tan(x/2)))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2)
Simplificación general [src] 
                          /    1     \                 /       2/x\        /x\\
       2               log|----------|              log|1 - tan |-| + 2*tan|-||
1   cos (x)   log(2)      \1 + cos(x)/   sin(2*x)      \        \2/        \2//
- - ------- - ------ - --------------- - -------- + ---------------------------
4      4        4             4             8                    4
−log⁡(1cos⁡(x)+1)4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)4−sin⁡(2x)8−cos⁡2(x)4−log⁡(2)4+14- \frac{\log{\left(\frac{1}{\cos{\left(x \right)} + 1} \right)}}{4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{4} - \frac{\sin{\left(2 x \right)}}{8} - \frac{\cos^{2}{\left(x \right)}}{4} - \frac{\log{\left(2 \right)}}{4} + \frac{1}{4} 
1/4 - cos(x)^2/4 - log(2)/4 - log(1/(1 + cos(x)))/4 - sin(2*x)/8 + log(1 - tan(x/2)^2 + 2*tan(x/2))/4
Respuesta numérica [src] 
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 2.0*tan(x/2)^3/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 4.0*tan(x/2)^2/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - 2.0*tan(x/2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 2.0*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - 2.0*tan(x/2)^2*log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2)
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 2.0*tan(x/2)^3/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 4.0*tan(x/2)^2/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - 2.0*tan(x/2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) + 2.0*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2) - 2.0*tan(x/2)^2*log(1 + tan(x/2)^2)/(4.0 + 4.0*tan(x/2)^4 + 8.0*tan(x/2)^2)
Denominador común [src] 
     /       2/x\\      /       2/x\        /x\\      3/x\      /x\        2/x\
  log|1 + tan |-||   log|1 - tan |-| + 2*tan|-||   tan |-| - tan|-| + 2*tan |-|
     \        \2//      \        \2/        \2//       \2/      \2/         \2/
- ---------------- + --------------------------- + ----------------------------
         4                        4                          4/x\        2/x\  
                                                    2 + 2*tan |-| + 4*tan |-|  
                                                              \2/         \2/
tan⁡3(x2)+2tan⁡2(x2)−tan⁡(x2)2tan⁡4(x2)+4tan⁡2(x2)+2−log⁡(tan⁡2(x2)+1)4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)4\frac{\tan^{3}{\left(\frac{x}{2} \right)} + 2 \tan^{2}{\left(\frac{x}{2} \right)} - \tan{\left(\frac{x}{2} \right)}}{2 \tan^{4}{\left(\frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{2} \right)} + 2} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{4} 
-log(1 + tan(x/2)^2)/4 + log(1 - tan(x/2)^2 + 2*tan(x/2))/4 + (tan(x/2)^3 - tan(x/2) + 2*tan(x/2)^2)/(2 + 2*tan(x/2)^4 + 4*tan(x/2)^2)
Denominador racional [src] 
     /       2/x\\        /x\        3/x\        2/x\      4/x\    /       2/x\        /x\\      4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\      /       2/x\        /x\\
- log|1 + tan |-|| - 2*tan|-| + 2*tan |-| + 4*tan |-| + tan |-|*log|1 - tan |-| + 2*tan|-|| - tan |-|*log|1 + tan |-|| - 2*tan |-|*log|1 + tan |-|| + 2*tan |-|*log|1 - tan |-| + 2*tan|-|| + log|1 - tan |-| + 2*tan|-||
     \        \2//        \2/         \2/         \2/       \2/    \        \2/        \2//       \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//      \        \2/        \2//
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                                                                                                         4/x\        2/x\                                                                                                
                                                                                                4 + 4*tan |-| + 8*tan |-|                                                                                                
                                                                                                          \2/         \2/
−log⁡(tan⁡2(x2)+1)tan⁡4(x2)−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)−log⁡(tan⁡2(x2)+1)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡4(x2)+2log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡2(x2)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)+2tan⁡3(x2)+4tan⁡2(x2)−2tan⁡(x2)4tan⁡4(x2)+8tan⁡2(x2)+4\frac{- \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} - 2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} + 2 \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} + 2 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} 
(-log(1 + tan(x/2)^2) - 2*tan(x/2) + 2*tan(x/2)^3 + 4*tan(x/2)^2 + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2)) - tan(x/2)^4*log(1 + tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2)) + log(1 - tan(x/2)^2 + 2*tan(x/2)))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2)
Unión de expresiones racionales [src] 
     /       2/x\\        /x\        3/x\        2/x\      4/x\    /       2/x\        /x\\      4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\      /       2/x\        /x\\
- log|1 + tan |-|| - 2*tan|-| + 2*tan |-| + 4*tan |-| + tan |-|*log|1 - tan |-| + 2*tan|-|| - tan |-|*log|1 + tan |-|| - 2*tan |-|*log|1 + tan |-|| + 2*tan |-|*log|1 - tan |-| + 2*tan|-|| + log|1 - tan |-| + 2*tan|-||
     \        \2//        \2/         \2/         \2/       \2/    \        \2/        \2//       \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//      \        \2/        \2//
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 /       4/x\        2/x\\                                                                                               
                                                                                               4*|1 + tan |-| + 2*tan |-||                                                                                               
                                                                                                 \        \2/         \2//
−log⁡(tan⁡2(x2)+1)tan⁡4(x2)−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)−log⁡(tan⁡2(x2)+1)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡4(x2)+2log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡2(x2)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)+2tan⁡3(x2)+4tan⁡2(x2)−2tan⁡(x2)4(tan⁡4(x2)+2tan⁡2(x2)+1)\frac{- \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} - 2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} + 2 \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} + 2 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}}{4 \left(\tan^{4}{\left(\frac{x}{2} \right)} + 2 \tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
(-log(1 + tan(x/2)^2) - 2*tan(x/2) + 2*tan(x/2)^3 + 4*tan(x/2)^2 + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2)) - tan(x/2)^4*log(1 + tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2)) + log(1 - tan(x/2)^2 + 2*tan(x/2)))/(4*(1 + tan(x/2)^4 + 2*tan(x/2)^2))
Potencias [src] 
   /                     2                        \                /                     2\                                                                                                        /                     2                        \                                   /                     2\                                                                                                                                                                              /                     2                        \                                    /                     2\         
   |    /   I*x    -I*x \        /   I*x    -I*x \|                |    /   I*x    -I*x \ |                                                                                                   4    |    /   I*x    -I*x \        /   I*x    -I*x \|                              4    |    /   I*x    -I*x \ |                                                                                                                                                                         2    |    /   I*x    -I*x \        /   I*x    -I*x \|                               2    |    /   I*x    -I*x \ |         
   |    |   ---    -----|        |   ---    -----||                |    |   ---    -----| |                                                                                  /   I*x    -I*x \     |    |   ---    -----|        |   ---    -----||             /   I*x    -I*x \     |    |   ---    -----| |                                                                                                                                                        /   I*x    -I*x \     |    |   ---    -----|        |   ---    -----||              /   I*x    -I*x \     |    |   ---    -----| |         
   |    |    2       2  |        |    2       2  ||                |    |    2       2  | |                                                                                  |   ---    -----|     |    |    2       2  |        |    2       2  ||             |   ---    -----|     |    |    2       2  | |                                                                                                                                                        |   ---    -----|     |    |    2       2  |        |    2       2  ||              |   ---    -----|     |    |    2       2  | |         
   |    \- e    + e     /    2*I*\- e    + e     /|                |    \- e    + e     / |                                                                                  |    2       2  |     |    \- e    + e     /    2*I*\- e    + e     /|             |    2       2  |     |    \- e    + e     / |                                                                                                                                                        |    2       2  |     |    \- e    + e     /    2*I*\- e    + e     /|              |    2       2  |     |    \- e    + e     / |         
log|1 + ------------------ + ---------------------|             log|1 - ------------------|                                                                                  \- e    + e     / *log|1 + ------------------ + ---------------------|             \- e    + e     / *log|1 - ------------------|                                                                                                                                                      2*\- e    + e     / *log|1 + ------------------ + ---------------------|            2*\- e    + e     / *log|1 - ------------------|         
   |                    2         I*x    -I*x     |                |                    2 |                                                       2                                                |                    2         I*x    -I*x     |                                   |                    2 |                                                        3                                                                                                                     |                    2         I*x    -I*x     |                                    |                    2 |         
   |     / I*x    -I*x \          ---    -----    |                |     / I*x    -I*x \  |                                      /   I*x    -I*x \                                                 |     / I*x    -I*x \          ---    -----    |                                   |     / I*x    -I*x \  |                                       /   I*x    -I*x \                                                    /   I*x    -I*x \                                                 |     / I*x    -I*x \          ---    -----    |                                    |     / I*x    -I*x \  |         
   |     | ---    -----|           2       2      |                |     | ---    -----|  |                                      |   ---    -----|                                                 |     | ---    -----|           2       2      |                                   |     | ---    -----|  |                                       |   ---    -----|                                                    |   ---    -----|                                                 |     | ---    -----|           2       2      |                                    |     | ---    -----|  |         
   |     |  2       2  |         e    + e         |                |     |  2       2  |  |                                      |    2       2  |                                                 |     |  2       2  |         e    + e         |                                   |     |  2       2  |  |                                       |    2       2  |                                                    |    2       2  |                                                 |     |  2       2  |         e    + e         |                                    |     |  2       2  |  |         
   \     \e    + e     /                          /                \     \e    + e     /  /                                    4*\- e    + e     /                                                 \     \e    + e     /                          /                                   \     \e    + e     /  /                                   2*I*\- e    + e     /                                                2*I*\- e    + e     /                                                 \     \e    + e     /                          /                                    \     \e    + e     /  /         
--------------------------------------------------- - ----------------------------------------------- - ------------------------------------------------------------------ + ---------------------------------------------------------------------- - ------------------------------------------------------------------ - ------------------------------------------------------------------ - ----------------------------------------------------------------- - ------------------------------------------------------------------------ + ------------------------------------------------------------------
                         2                      4                            2                      4                    /                       2                      4\                      /                       2                      4\                      /                       2                      4\                    /                       2                      4\                   /                       2                      4\                       /                       2                      4\                       /                       2                      4\
        /   I*x    -I*x \      /   I*x    -I*x \            /   I*x    -I*x \      /   I*x    -I*x \                   2 |      /   I*x    -I*x \      /   I*x    -I*x \ |                    4 |      /   I*x    -I*x \      /   I*x    -I*x \ |                    4 |      /   I*x    -I*x \      /   I*x    -I*x \ |                  3 |      /   I*x    -I*x \      /   I*x    -I*x \ |                   |      /   I*x    -I*x \      /   I*x    -I*x \ |                     2 |      /   I*x    -I*x \      /   I*x    -I*x \ |                     2 |      /   I*x    -I*x \      /   I*x    -I*x \ |
        |   ---    -----|      |   ---    -----|            |   ---    -----|      |   ---    -----|    / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |     / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |     / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |   / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |   / I*x    -I*x \ |      |   ---    -----|      |   ---    -----| |      / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |      / I*x    -I*x \  |      |   ---    -----|      |   ---    -----| |
        |    2       2  |      |    2       2  |            |    2       2  |      |    2       2  |    | ---    -----|  |      |    2       2  |      |    2       2  | |     | ---    -----|  |      |    2       2  |      |    2       2  | |     | ---    -----|  |      |    2       2  |      |    2       2  | |   | ---    -----|  |      |    2       2  |      |    2       2  | |   | ---    -----| |      |    2       2  |      |    2       2  | |      | ---    -----|  |      |    2       2  |      |    2       2  | |      | ---    -----|  |      |    2       2  |      |    2       2  | |
      8*\- e    + e     /    4*\- e    + e     /          8*\- e    + e     /    4*\- e    + e     /    |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |     |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |     |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |   |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |   |  2       2  | |    8*\- e    + e     /    4*\- e    + e     / |      |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |      |  2       2  |  |    8*\- e    + e     /    4*\- e    + e     / |
  4 - -------------------- + --------------------     4 - -------------------- + --------------------   \e    + e     / *|4 - -------------------- + --------------------|     \e    + e     / *|4 - -------------------- + --------------------|     \e    + e     / *|4 - -------------------- + --------------------|   \e    + e     / *|4 - -------------------- + --------------------|   \e    + e     /*|4 - -------------------- + --------------------|      \e    + e     / *|4 - -------------------- + --------------------|      \e    + e     / *|4 - -------------------- + --------------------|
                       2                      4                            2                      4                      |                     2                      4  |                      |                     2                      4  |                      |                     2                      4  |                    |                     2                      4  |                   |                     2                      4  |                       |                     2                      4  |                       |                     2                      4  |
        / I*x    -I*x \        / I*x    -I*x \              / I*x    -I*x \        / I*x    -I*x \                       |      / I*x    -I*x \        / I*x    -I*x \   |                      |      / I*x    -I*x \        / I*x    -I*x \   |                      |      / I*x    -I*x \        / I*x    -I*x \   |                    |      / I*x    -I*x \        / I*x    -I*x \   |                   |      / I*x    -I*x \        / I*x    -I*x \   |                       |      / I*x    -I*x \        / I*x    -I*x \   |                       |      / I*x    -I*x \        / I*x    -I*x \   |
        | ---    -----|        | ---    -----|              | ---    -----|        | ---    -----|                       |      | ---    -----|        | ---    -----|   |                      |      | ---    -----|        | ---    -----|   |                      |      | ---    -----|        | ---    -----|   |                    |      | ---    -----|        | ---    -----|   |                   |      | ---    -----|        | ---    -----|   |                       |      | ---    -----|        | ---    -----|   |                       |      | ---    -----|        | ---    -----|   |
        |  2       2  |        |  2       2  |              |  2       2  |        |  2       2  |                       |      |  2       2  |        |  2       2  |   |                      |      |  2       2  |        |  2       2  |   |                      |      |  2       2  |        |  2       2  |   |                    |      |  2       2  |        |  2       2  |   |                   |      |  2       2  |        |  2       2  |   |                       |      |  2       2  |        |  2       2  |   |                       |      |  2       2  |        |  2       2  |   |
        \e    + e     /        \e    + e     /              \e    + e     /        \e    + e     /                       \      \e    + e     /        \e    + e     /   /                      \      \e    + e     /        \e    + e     /   /                      \      \e    + e     /        \e    + e     /   /                    \      \e    + e     /        \e    + e     /   /                   \      \e    + e     /        \e    + e     /   /                       \      \e    + e     /        \e    + e     /   /                       \      \e    + e     /        \e    + e     /   /
−(−eix2+e−ix2)4log⁡(−(−eix2+e−ix2)2(eix2+e−ix2)2+1)(eix2+e−ix2)4(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)+(−eix2+e−ix2)4log⁡((−eix2+e−ix2)2(eix2+e−ix2)2+2i(−eix2+e−ix2)eix2+e−ix2+1)(eix2+e−ix2)4(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)−2i(−eix2+e−ix2)3(eix2+e−ix2)3(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)+2(−eix2+e−ix2)2log⁡(−(−eix2+e−ix2)2(eix2+e−ix2)2+1)(eix2+e−ix2)2(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)−2(−eix2+e−ix2)2log⁡((−eix2+e−ix2)2(eix2+e−ix2)2+2i(−eix2+e−ix2)eix2+e−ix2+1)(eix2+e−ix2)2(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)−4(−eix2+e−ix2)2(eix2+e−ix2)2(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)−2i(−eix2+e−ix2)(eix2+e−ix2)(4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4)−log⁡(−(−eix2+e−ix2)2(eix2+e−ix2)2+1)4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4+log⁡((−eix2+e−ix2)2(eix2+e−ix2)2+2i(−eix2+e−ix2)eix2+e−ix2+1)4(−eix2+e−ix2)4(eix2+e−ix2)4−8(−eix2+e−ix2)2(eix2+e−ix2)2+4- \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4} \log{\left(- \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 1 \right)}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} + \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4} \log{\left(\frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + \frac{2 i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1 \right)}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} - \frac{2 i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{3} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} + \frac{2 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \log{\left(- \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 1 \right)}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} - \frac{2 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \log{\left(\frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + \frac{2 i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1 \right)}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} - \frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2} \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} - \frac{2 i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right) \left(\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4\right)} - \frac{\log{\left(- \frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 1 \right)}}{\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4} + \frac{\log{\left(\frac{\left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + \frac{2 i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1 \right)}}{\frac{4 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{4}} - \frac{8 \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}}{\left(e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)^{2}} + 4} 
   /       2/x\        /x\\           /       2/x\\                     /x\                        3/x\                        2/x\              4/x\    /       2/x\        /x\\       4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\
log|1 - tan |-| + 2*tan|-||        log|1 + tan |-||                2*tan|-|                   2*tan |-|                   4*tan |-|           tan |-|*log|1 - tan |-| + 2*tan|-||    tan |-|*log|1 + tan |-||   2*tan |-|*log|1 + tan |-||   2*tan |-|*log|1 - tan |-| + 2*tan|-||
   \        \2/        \2//           \        \2//                     \2/                         \2/                         \2/               \2/    \        \2/        \2//        \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//
--------------------------- - ------------------------- - ------------------------- + ------------------------- + ------------------------- + ----------------------------------- - ------------------------- - -------------------------- + -------------------------------------
          4/x\        2/x\             4/x\        2/x\            4/x\        2/x\            4/x\        2/x\            4/x\        2/x\                 4/x\        2/x\                 4/x\        2/x\            4/x\        2/x\                   4/x\        2/x\      
 4 + 4*tan |-| + 8*tan |-|    4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|          4 + 4*tan |-| + 8*tan |-|      
           \2/         \2/              \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/                  \2/         \2/                  \2/         \2/             \2/         \2/                    \2/         \2/
−log⁡(tan⁡2(x2)+1)tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−log⁡(tan⁡2(x2)+1)4tan⁡4(x2)+8tan⁡2(x2)+4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+2log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)4tan⁡4(x2)+8tan⁡2(x2)+4+2tan⁡3(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+4tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2tan⁡(x2)4tan⁡4(x2)+8tan⁡2(x2)+4- \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} 
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^3/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 4*tan(x/2)^2/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2)
Combinatoria [src] 
     /       2/x\\        /x\        3/x\        2/x\      4/x\    /       2/x\        /x\\      4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\      /       2/x\        /x\\
- log|1 + tan |-|| - 2*tan|-| + 2*tan |-| + 4*tan |-| + tan |-|*log|1 - tan |-| + 2*tan|-|| - tan |-|*log|1 + tan |-|| - 2*tan |-|*log|1 + tan |-|| + 2*tan |-|*log|1 - tan |-| + 2*tan|-|| + log|1 - tan |-| + 2*tan|-||
     \        \2//        \2/         \2/         \2/       \2/    \        \2/        \2//       \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//      \        \2/        \2//
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                                                                                                       /       2/x\\                                                                                                     
                                                                                                     4*|1 + tan |-||                                                                                                     
                                                                                                       \        \2//
−log⁡(tan⁡2(x2)+1)tan⁡4(x2)−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)−log⁡(tan⁡2(x2)+1)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡4(x2)+2log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡2(x2)+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)+2tan⁡3(x2)+4tan⁡2(x2)−2tan⁡(x2)4(tan⁡2(x2)+1)2\frac{- \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} - 2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)} + 2 \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)} + \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} + 2 \tan^{3}{\left(\frac{x}{2} \right)} + 4 \tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}}{4 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} 
(-log(1 + tan(x/2)^2) - 2*tan(x/2) + 2*tan(x/2)^3 + 4*tan(x/2)^2 + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2)) - tan(x/2)^4*log(1 + tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2)) + log(1 - tan(x/2)^2 + 2*tan(x/2)))/(4*(1 + tan(x/2)^2)^2)
Compilar la expresión [src] 
   /       2/x\        /x\\           /       2/x\\                     /x\                        3/x\                        2/x\              4/x\    /       2/x\        /x\\       4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\
log|1 - tan |-| + 2*tan|-||        log|1 + tan |-||                2*tan|-|                   2*tan |-|                   4*tan |-|           tan |-|*log|1 - tan |-| + 2*tan|-||    tan |-|*log|1 + tan |-||   2*tan |-|*log|1 + tan |-||   2*tan |-|*log|1 - tan |-| + 2*tan|-||
   \        \2/        \2//           \        \2//                     \2/                         \2/                         \2/               \2/    \        \2/        \2//        \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//
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          4/x\        2/x\             4/x\        2/x\            4/x\        2/x\            4/x\        2/x\            4/x\        2/x\                 4/x\        2/x\                 4/x\        2/x\            4/x\        2/x\                   4/x\        2/x\      
 4 + 4*tan |-| + 8*tan |-|    4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|          4 + 4*tan |-| + 8*tan |-|      
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log⁡((1−tan⁡2(x2))+2tan⁡(x2))tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+2log⁡((1−tan⁡2(x2))+2tan⁡(x2))tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+log⁡((1−tan⁡2(x2))+2tan⁡(x2))4tan⁡4(x2)+8tan⁡2(x2)+4−log⁡(tan⁡2(x2)+1)tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−log⁡(tan⁡2(x2)+1)4tan⁡4(x2)+8tan⁡2(x2)+4+2tan⁡3(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+4tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2tan⁡(x2)4tan⁡4(x2)+8tan⁡2(x2)+4\frac{\log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) + 2 \tan{\left(\frac{x}{2} \right)} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} 
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^3/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 4*tan(x/2)^2/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2)
Abrimos la expresión [src] 
   /       2/x\        /x\\           /       2/x\\                     /x\                        3/x\                        2/x\              4/x\    /       2/x\        /x\\       4/x\    /       2/x\\        2/x\    /       2/x\\        2/x\    /       2/x\        /x\\
log|1 - tan |-| + 2*tan|-||        log|1 + tan |-||                2*tan|-|                   2*tan |-|                   4*tan |-|           tan |-|*log|1 - tan |-| + 2*tan|-||    tan |-|*log|1 + tan |-||   2*tan |-|*log|1 + tan |-||   2*tan |-|*log|1 - tan |-| + 2*tan|-||
   \        \2/        \2//           \        \2//                     \2/                         \2/                         \2/               \2/    \        \2/        \2//        \2/    \        \2//         \2/    \        \2//         \2/    \        \2/        \2//
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          4/x\        2/x\             4/x\        2/x\            4/x\        2/x\            4/x\        2/x\            4/x\        2/x\                 4/x\        2/x\                 4/x\        2/x\            4/x\        2/x\                   4/x\        2/x\      
 4 + 4*tan |-| + 8*tan |-|    4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|        4 + 4*tan |-| + 8*tan |-|   4 + 4*tan |-| + 8*tan |-|          4 + 4*tan |-| + 8*tan |-|      
           \2/         \2/              \2/         \2/             \2/         \2/             \2/         \2/             \2/         \2/                  \2/         \2/                  \2/         \2/             \2/         \2/                    \2/         \2/
−log⁡(tan⁡2(x2)+1)tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2log⁡(tan⁡2(x2)+1)tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−log⁡(tan⁡2(x2)+1)4tan⁡4(x2)+8tan⁡2(x2)+4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡4(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+2log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+log⁡(−tan⁡2(x2)+2tan⁡(x2)+1)4tan⁡4(x2)+8tan⁡2(x2)+4+2tan⁡3(x2)4tan⁡4(x2)+8tan⁡2(x2)+4+4tan⁡2(x2)4tan⁡4(x2)+8tan⁡2(x2)+4−2tan⁡(x2)4tan⁡4(x2)+8tan⁡2(x2)+4- \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{\log{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 2 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{4}{\left(\frac{x}{2} \right)} + 8 \tan^{2}{\left(\frac{x}{2} \right)} + 4} 
log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^3/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 4*tan(x/2)^2/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + tan(x/2)^4*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - tan(x/2)^4*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) - 2*tan(x/2)^2*log(1 + tan(x/2)^2)/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2) + 2*tan(x/2)^2*log(1 - tan(x/2)^2 + 2*tan(x/2))/(4 + 4*tan(x/2)^4 + 8*tan(x/2)^2)
    © Sr Examen – Калькулятор