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Resolución de integrales/ cosx^4/ x/cosx/ x/cosx^4

Integral de x/cosx^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |     x      
 |  ------- dx
 |     4      
 |  cos (x)   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{x}{\cos^{4}{\left(x \right)}}\, dx$$ 
Integral(x/cos(x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                    4/x\                                 /       /x\\                             /        /x\\                                2/x\                                 /       2/x\\                                 5/x\                                      /x\                            2/x\    /       2/x\\                    4/x\    /       /x\\                     4/x\    /        /x\\                    6/x\    /       2/x\\                    6/x\    /       /x\\                     6/x\    /        /x\\                             3/x\                            2/x\    /       /x\\                     2/x\    /        /x\\                    4/x\    /       2/x\\      
 |                                2*tan |-|                            2*log|1 + tan|-||                        2*log|-1 + tan|-||                           2*tan |-|                            2*log|1 + tan |-||                          6*x*tan |-|                               6*x*tan|-|                       6*tan |-|*log|1 + tan |-||               6*tan |-|*log|1 + tan|-||                6*tan |-|*log|-1 + tan|-||               2*tan |-|*log|1 + tan |-||               2*tan |-|*log|1 + tan|-||                2*tan |-|*log|-1 + tan|-||                      4*x*tan |-|                       6*tan |-|*log|1 + tan|-||                6*tan |-|*log|-1 + tan|-||               6*tan |-|*log|1 + tan |-||      
 |    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//      
 | ------- dx = C - -------------------------------------- - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + --------------------------------------
 |    4                       4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\             4/x\        6/x\        2/x\
 | cos (x)          -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|   -3 - 9*tan |-| + 3*tan |-| + 9*tan |-|
 |                             \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/              \2/         \2/         \2/              \2/         \2/         \2/              \2/         \2/         \2/              \2/         \2/         \2/              \2/         \2/         \2/
/
$$\int \frac{x}{\cos^{4}{\left(x \right)}}\, dx = C - \frac{6 x \tan^{5}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{4 x \tan^{3}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{6 x \tan{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{6 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{6 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{6 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{2 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} - \frac{2 \tan^{4}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3} + \frac{2 \tan^{2}{\left(\frac{x}{2} \right)}}{3 \tan^{6}{\left(\frac{x}{2} \right)} - 9 \tan^{4}{\left(\frac{x}{2} \right)} + 9 \tan^{2}{\left(\frac{x}{2} \right)} - 3}$$
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Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                       5                                                                                             4                                                                                                                                            2                                          /       2     \                                    3                                              2         /       2     \                  4                                                  4                                              6         /       2     \                  6                                                  6                                          2                                                  2                                              4         /       2     \       
                  6*tan (1/2)                                     6*tan(1/2)                                    2*tan (1/2)                            2*(pi*I + log(1 - tan(1/2)))                       2*log(1 + tan(1/2))                                2*tan (1/2)                                2*log\1 + tan (1/2)/                               4*tan (1/2)                    2*pi*I          6*tan (1/2)*log\1 + tan (1/2)/             6*tan (1/2)*(pi*I + log(1 - tan(1/2)))             6*tan (1/2)*log(1 + tan(1/2))                  2*tan (1/2)*log\1 + tan (1/2)/             2*tan (1/2)*(pi*I + log(1 - tan(1/2)))             2*tan (1/2)*log(1 + tan(1/2))              6*tan (1/2)*(pi*I + log(1 - tan(1/2)))             6*tan (1/2)*log(1 + tan(1/2))                  6*tan (1/2)*log\1 + tan (1/2)/       
- -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- - ------ - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + --------------------------------------------
            4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2          3                4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2     
  -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)            -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)
$$\frac{6 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{4 \tan^{3}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{6 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \tan^{5}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \tan{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{6 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 i \pi}{3} + \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right)}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}}$$ 
=
= 
                       5                                                                                             4                                                                                                                                            2                                          /       2     \                                    3                                              2         /       2     \                  4                                                  4                                              6         /       2     \                  6                                                  6                                          2                                                  2                                              4         /       2     \       
                  6*tan (1/2)                                     6*tan(1/2)                                    2*tan (1/2)                            2*(pi*I + log(1 - tan(1/2)))                       2*log(1 + tan(1/2))                                2*tan (1/2)                                2*log\1 + tan (1/2)/                               4*tan (1/2)                    2*pi*I          6*tan (1/2)*log\1 + tan (1/2)/             6*tan (1/2)*(pi*I + log(1 - tan(1/2)))             6*tan (1/2)*log(1 + tan(1/2))                  2*tan (1/2)*log\1 + tan (1/2)/             2*tan (1/2)*(pi*I + log(1 - tan(1/2)))             2*tan (1/2)*log(1 + tan(1/2))              6*tan (1/2)*(pi*I + log(1 - tan(1/2)))             6*tan (1/2)*log(1 + tan(1/2))                  6*tan (1/2)*log\1 + tan (1/2)/       
- -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- - ------ - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + -------------------------------------------- + --------------------------------------------
            4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2          3                4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2                  4             6             2     
  -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)            -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)   -3 - 9*tan (1/2) + 3*tan (1/2) + 9*tan (1/2)
$$\frac{6 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{4 \tan^{3}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{6 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \tan^{5}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \tan{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{6 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 i \pi}{3} + \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{6}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{6 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{4}{\left(\frac{1}{2} \right)}}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right)}{-3 - 9 \tan^{4}{\left(\frac{1}{2} \right)} + 3 \tan^{6}{\left(\frac{1}{2} \right)} + 9 \tan^{2}{\left(\frac{1}{2} \right)}}$$ 
-6*tan(1/2)^5/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 6*tan(1/2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 2*tan(1/2)^4/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 2*(pi*i + log(1 - tan(1/2)))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 2*log(1 + tan(1/2))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 2*tan(1/2)^2/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 2*log(1 + tan(1/2)^2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 4*tan(1/2)^3/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 2*pi*i/3 - 6*tan(1/2)^2*log(1 + tan(1/2)^2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 6*tan(1/2)^4*(pi*i + log(1 - tan(1/2)))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 6*tan(1/2)^4*log(1 + tan(1/2))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 2*tan(1/2)^6*log(1 + tan(1/2)^2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 2*tan(1/2)^6*(pi*i + log(1 - tan(1/2)))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 2*tan(1/2)^6*log(1 + tan(1/2))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 6*tan(1/2)^2*(pi*i + log(1 - tan(1/2)))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 6*tan(1/2)^2*log(1 + tan(1/2))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 6*tan(1/2)^4*log(1 + tan(1/2)^2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2)
Respuesta numérica [src] 
2.00191085687268
2.00191085687268

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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