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Resolución de integrales/ (7*cos(2x))/(cos(x)+sin(x))

Integral de (7*cos(2x))/(cos(x)+sin(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |     7*cos(2*x)     
 |  --------------- dx
 |  cos(x) + sin(x)   
 |                    
/                     
0
∫017cos⁡(2x)sin⁡(x)+cos⁡(x) dx\int\limits_{0}^{1} \frac{7 \cos{\left(2 x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx 
Integral((7*cos(2*x))/(cos(x) + sin(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                 /x\         ___    /       ___      /x\\       ___    /       ___      /x\\        ___    /       ___      /x\\        ___    /       ___      /x\\        ___    2/x\    /       ___      /x\\        ___    2/x\    /       ___      /x\\
 |                                            56*tan|-|     7*\/ 2 *log|-1 + \/ 2  + tan|-||   7*\/ 2 *log|-1 - \/ 2  + tan|-||   14*\/ 2 *log|-1 - \/ 2  + tan|-||   14*\/ 2 *log|-1 + \/ 2  + tan|-||   14*\/ 2 *tan |-|*log|-1 - \/ 2  + tan|-||   14*\/ 2 *tan |-|*log|-1 + \/ 2  + tan|-||
 |    7*cos(2*x)                  56                \2/                \                \2//              \                \2//               \                \2//               \                \2//                \2/    \                \2//                \2/    \                \2//
 | --------------- dx = C + ------------- + ------------- - -------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - ----------------------------------------- + -----------------------------------------
 | cos(x) + sin(x)                   2/x\            2/x\                  2                                  2                                      2/x\                                2/x\                                    2/x\                                        2/x\              
 |                          4 + 4*tan |-|   4 + 4*tan |-|                                                                                   4 + 4*tan |-|                       4 + 4*tan |-|                           4 + 4*tan |-|                               4 + 4*tan |-|              
/                                     \2/             \2/                                                                                             \2/                                 \2/                                     \2/                                         \2/
∫7cos⁡(2x)sin⁡(x)+cos⁡(x) dx=C−72log⁡(tan⁡(x2)−1+2)2+72log⁡(tan⁡(x2)−2−1)2+142log⁡(tan⁡(x2)−1+2)tan⁡2(x2)4tan⁡2(x2)+4+142log⁡(tan⁡(x2)−1+2)4tan⁡2(x2)+4−142log⁡(tan⁡(x2)−2−1)tan⁡2(x2)4tan⁡2(x2)+4−142log⁡(tan⁡(x2)−2−1)4tan⁡2(x2)+4+56tan⁡(x2)4tan⁡2(x2)+4+564tan⁡2(x2)+4\int \frac{7 \cos{\left(2 x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C - \frac{7 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{2} + \frac{7 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{2} + \frac{14 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{14 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 + \sqrt{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{14 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} - \frac{14 \sqrt{2} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2} - 1 \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{56 \tan{\left(\frac{x}{2} \right)}}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4} + \frac{56}{4 \tan^{2}{\left(\frac{x}{2} \right)} + 4}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-2020
Trazar el gráfico f(x)
Respuesta [src] 
                                              ___    /       ___           \       ___ /          /      ___           \\        ___ /          /      ___           \\        ___    /       ___           \        ___    2      /          /      ___           \\        ___    2         /       ___           \
             56           56*tan(1/2)     7*\/ 2 *log\-1 + \/ 2  + tan(1/2)/   7*\/ 2 *\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *log\-1 + \/ 2  + tan(1/2)/   14*\/ 2 *tan (1/2)*\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *tan (1/2)*log\-1 + \/ 2  + tan(1/2)/
-14 + --------------- + --------------- - ---------------------------------- + ------------------------------------------ - ------------------------------------------- + ----------------------------------- - ----------------------------------------------------- + ---------------------------------------------
               2                 2                        2                                        2                                               2                                         2                                              2                                                   2                    
      4 + 4*tan (1/2)   4 + 4*tan (1/2)                                                                                                   4 + 4*tan (1/2)                           4 + 4*tan (1/2)                                4 + 4*tan (1/2)                                     4 + 4*tan (1/2)
−14+142log⁡(−1+tan⁡(12)+2)4tan⁡2(12)+4+142log⁡(−1+tan⁡(12)+2)tan⁡2(12)4tan⁡2(12)+4−72log⁡(−1+tan⁡(12)+2)2+56tan⁡(12)4tan⁡2(12)+4+564tan⁡2(12)+4−142(log⁡(−tan⁡(12)+1+2)+iπ)4tan⁡2(12)+4−142(log⁡(−tan⁡(12)+1+2)+iπ)tan⁡2(12)4tan⁡2(12)+4+72(log⁡(−tan⁡(12)+1+2)+iπ)2-14 + \frac{14 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{14 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{7 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{2} + \frac{56 \tan{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{56}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{14 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{14 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{7 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} 
=
= 
                                              ___    /       ___           \       ___ /          /      ___           \\        ___ /          /      ___           \\        ___    /       ___           \        ___    2      /          /      ___           \\        ___    2         /       ___           \
             56           56*tan(1/2)     7*\/ 2 *log\-1 + \/ 2  + tan(1/2)/   7*\/ 2 *\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *log\-1 + \/ 2  + tan(1/2)/   14*\/ 2 *tan (1/2)*\pi*I + log\1 + \/ 2  - tan(1/2)//   14*\/ 2 *tan (1/2)*log\-1 + \/ 2  + tan(1/2)/
-14 + --------------- + --------------- - ---------------------------------- + ------------------------------------------ - ------------------------------------------- + ----------------------------------- - ----------------------------------------------------- + ---------------------------------------------
               2                 2                        2                                        2                                               2                                         2                                              2                                                   2                    
      4 + 4*tan (1/2)   4 + 4*tan (1/2)                                                                                                   4 + 4*tan (1/2)                           4 + 4*tan (1/2)                                4 + 4*tan (1/2)                                     4 + 4*tan (1/2)
−14+142log⁡(−1+tan⁡(12)+2)4tan⁡2(12)+4+142log⁡(−1+tan⁡(12)+2)tan⁡2(12)4tan⁡2(12)+4−72log⁡(−1+tan⁡(12)+2)2+56tan⁡(12)4tan⁡2(12)+4+564tan⁡2(12)+4−142(log⁡(−tan⁡(12)+1+2)+iπ)4tan⁡2(12)+4−142(log⁡(−tan⁡(12)+1+2)+iπ)tan⁡2(12)4tan⁡2(12)+4+72(log⁡(−tan⁡(12)+1+2)+iπ)2-14 + \frac{14 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{14 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{7 \sqrt{2} \log{\left(-1 + \tan{\left(\frac{1}{2} \right)} + \sqrt{2} \right)}}{2} + \frac{56 \tan{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{56}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{14 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} - \frac{14 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{4 \tan^{2}{\left(\frac{1}{2} \right)} + 4} + \frac{7 \sqrt{2} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 1 + \sqrt{2} \right)} + i \pi\right)}{2} 
-14 + 56/(4 + 4*tan(1/2)^2) + 56*tan(1/2)/(4 + 4*tan(1/2)^2) - 7*sqrt(2)*log(-1 + sqrt(2) + tan(1/2))/2 + 7*sqrt(2)*(pi*i + log(1 + sqrt(2) - tan(1/2)))/2 - 14*sqrt(2)*(pi*i + log(1 + sqrt(2) - tan(1/2)))/(4 + 4*tan(1/2)^2) + 14*sqrt(2)*log(-1 + sqrt(2) + tan(1/2))/(4 + 4*tan(1/2)^2) - 14*sqrt(2)*tan(1/2)^2*(pi*i + log(1 + sqrt(2) - tan(1/2)))/(4 + 4*tan(1/2)^2) + 14*sqrt(2)*tan(1/2)^2*log(-1 + sqrt(2) + tan(1/2))/(4 + 4*tan(1/2)^2)
Respuesta numérica [src] 
2.67241303473225
2.67241303473225

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

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