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Resolución de integrales/ cos^2/ 2y/cos^2(y)^2

Integral de 2y/cos^2(y)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |    2*y     
 |  ------- dy
 |     4      
 |  cos (y)   
 |            
/             
0
∫012ycos⁡4(y) dy\int\limits_{0}^{1} \frac{2 y}{\cos^{4}{\left(y \right)}}\, dy 
Integral((2*y)/cos(y)^4, (y, 0, 1))
Respuesta (Indefinida) [src] 
  /                                    4/y\                                 /       /y\\                             /        /y\\                                2/y\                                 /       2/y\\                                  5/y\                                     /y\                            2/y\    /       2/y\\                     4/y\    /       /y\\                    4/y\    /        /y\\                    6/y\    /       2/y\\                    6/y\    /       /y\\                     6/y\    /        /y\\                             3/y\                             2/y\    /       /y\\                    2/y\    /        /y\\                    4/y\    /       2/y\\      
 |                                4*tan |-|                            4*log|1 + tan|-||                        4*log|-1 + tan|-||                           4*tan |-|                            4*log|1 + tan |-||                          12*y*tan |-|                             12*y*tan|-|                      12*tan |-|*log|1 + tan |-||               12*tan |-|*log|1 + tan|-||              12*tan |-|*log|-1 + tan|-||               4*tan |-|*log|1 + tan |-||               4*tan |-|*log|1 + tan|-||                4*tan |-|*log|-1 + tan|-||                      8*y*tan |-|                       12*tan |-|*log|1 + tan|-||              12*tan |-|*log|-1 + tan|-||              12*tan |-|*log|1 + tan |-||      
 |   2*y                                \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//      
 | ------- dy = C - -------------------------------------- - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- - -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + -------------------------------------- + --------------------------------------
 |    4                       4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\             4/y\        6/y\        2/y\
 | cos (y)          -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/
/
∫2ycos⁡4(y) dy=C−12ytan⁡5(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+8ytan⁡3(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−12ytan⁡(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+4log⁡(tan⁡(y2)−1)tan⁡6(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−12log⁡(tan⁡(y2)−1)tan⁡4(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+12log⁡(tan⁡(y2)−1)tan⁡2(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−4log⁡(tan⁡(y2)−1)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+4log⁡(tan⁡(y2)+1)tan⁡6(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−12log⁡(tan⁡(y2)+1)tan⁡4(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+12log⁡(tan⁡(y2)+1)tan⁡2(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−4log⁡(tan⁡(y2)+1)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−4log⁡(tan⁡2(y2)+1)tan⁡6(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+12log⁡(tan⁡2(y2)+1)tan⁡4(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−12log⁡(tan⁡2(y2)+1)tan⁡2(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+4log⁡(tan⁡2(y2)+1)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3−4tan⁡4(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3+4tan⁡2(y2)3tan⁡6(y2)−9tan⁡4(y2)+9tan⁡2(y2)−3\int \frac{2 y}{\cos^{4}{\left(y \right)}}\, dy = C - \frac{12 y \tan^{5}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{8 y \tan^{3}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{12 y \tan{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{4 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{12 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{12 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{4 \log{\left(\tan{\left(\frac{y}{2} \right)} - 1 \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{4 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{12 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{12 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{4 \log{\left(\tan{\left(\frac{y}{2} \right)} + 1 \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{4 \log{\left(\tan^{2}{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{12 \log{\left(\tan^{2}{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{12 \log{\left(\tan^{2}{\left(\frac{y}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{4 \log{\left(\tan^{2}{\left(\frac{y}{2} \right)} + 1 \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} - \frac{4 \tan^{4}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3} + \frac{4 \tan^{2}{\left(\frac{y}{2} \right)}}{3 \tan^{6}{\left(\frac{y}{2} \right)} - 9 \tan^{4}{\left(\frac{y}{2} \right)} + 9 \tan^{2}{\left(\frac{y}{2} \right)} - 3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90025
Trazar el gráfico f(x)
Respuesta [src] 
                        5                                                                                            4                                                                                                                                            2                                          /       2     \                                    3                                              2         /       2     \                  4                                                   4                                             6         /       2     \                  6                                                  6                                          2                                                   2                                             4         /       2     \       
                  12*tan (1/2)                                   12*tan(1/2)                                    4*tan (1/2)                            4*(pi*I + log(1 - tan(1/2)))                       4*log(1 + tan(1/2))                                4*tan (1/2)                                4*log\1 + tan (1/2)/                               8*tan (1/2)                    4*pi*I         12*tan (1/2)*log\1 + tan (1/2)/            12*tan (1/2)*(pi*I + log(1 - tan(1/2)))             12*tan (1/2)*log(1 + tan(1/2))                 4*tan (1/2)*log\1 + tan (1/2)/             4*tan (1/2)*(pi*I + log(1 - tan(1/2)))             4*tan (1/2)*log(1 + tan(1/2))             12*tan (1/2)*(pi*I + log(1 - tan(1/2)))             12*tan (1/2)*log(1 + tan(1/2))                12*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)
12log⁡(tan⁡(12)+1)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+8tan⁡3(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4log⁡(tan⁡2(12)+1)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+12log⁡(tan⁡2(12)+1)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4log⁡(tan⁡(12)+1)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4log⁡(tan⁡2(12)+1)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12log⁡(tan⁡(12)+1)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12tan⁡5(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12log⁡(tan⁡2(12)+1)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4log⁡(tan⁡(12)+1)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12tan⁡(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+12(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4iπ3+4(log⁡(1−tan⁡(12))+iπ)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12(log⁡(1−tan⁡(12))+iπ)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4(log⁡(1−tan⁡(12))+iπ)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)\frac{12 \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{8 \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{4 \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 \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{12 \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{4 \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{4 \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{4 \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{12 \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{12 \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{12 \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{4 \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{12 \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{12 \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{4 i \pi}{3} + \frac{4 \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{12 \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{4 \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     \       
                  12*tan (1/2)                                   12*tan(1/2)                                    4*tan (1/2)                            4*(pi*I + log(1 - tan(1/2)))                       4*log(1 + tan(1/2))                                4*tan (1/2)                                4*log\1 + tan (1/2)/                               8*tan (1/2)                    4*pi*I         12*tan (1/2)*log\1 + tan (1/2)/            12*tan (1/2)*(pi*I + log(1 - tan(1/2)))             12*tan (1/2)*log(1 + tan(1/2))                 4*tan (1/2)*log\1 + tan (1/2)/             4*tan (1/2)*(pi*I + log(1 - tan(1/2)))             4*tan (1/2)*log(1 + tan(1/2))             12*tan (1/2)*(pi*I + log(1 - tan(1/2)))             12*tan (1/2)*log(1 + tan(1/2))                12*tan (1/2)*log\1 + tan (1/2)/       
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            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)
12log⁡(tan⁡(12)+1)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+8tan⁡3(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4log⁡(tan⁡2(12)+1)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+12log⁡(tan⁡2(12)+1)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+4log⁡(tan⁡(12)+1)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4log⁡(tan⁡2(12)+1)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12log⁡(tan⁡(12)+1)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12tan⁡5(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12log⁡(tan⁡2(12)+1)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4log⁡(tan⁡(12)+1)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12tan⁡(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)+12(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4iπ3+4(log⁡(1−tan⁡(12))+iπ)tan⁡6(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−12(log⁡(1−tan⁡(12))+iπ)tan⁡4(12)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)−4(log⁡(1−tan⁡(12))+iπ)−3−9tan⁡4(12)+3tan⁡6(12)+9tan⁡2(12)\frac{12 \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{8 \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{4 \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 \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{12 \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{4 \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{4 \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{4 \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{12 \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{12 \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{12 \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{4 \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{12 \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{12 \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{4 i \pi}{3} + \frac{4 \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{12 \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{4 \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)}} 
-12*tan(1/2)^5/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 12*tan(1/2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 4*tan(1/2)^4/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^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) - 4*log(1 + tan(1/2))/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 4*tan(1/2)^2/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 4*log(1 + tan(1/2)^2)/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) + 8*tan(1/2)^3/(-3 - 9*tan(1/2)^4 + 3*tan(1/2)^6 + 9*tan(1/2)^2) - 4*pi*i/3 - 12*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) - 12*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) - 12*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) - 4*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) + 4*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) + 4*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) + 12*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) + 12*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) + 12*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] 
4.00382171374537
4.00382171374537

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

    © Sr Examen – Калькулятор