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Resolución de integrales/ cos^2/ dx/(cos^2)5x

Integral de dx/(cos^2)5x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1             
  /             
 |              
 |     5        
 |  -------*x dx
 |     2        
 |  cos (x)     
 |              
/               
0
∫01x5cos⁡2(x) dx\int\limits_{0}^{1} x \frac{5}{\cos^{2}{\left(x \right)}}\, dx 
Integral((5/cos(x)^2)*x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                        /       /x\\        /        /x\\        /       2/x\\           /x\         2/x\    /       2/x\\        2/x\    /       /x\\        2/x\    /        /x\\
 |                    5*log|1 + tan|-||   5*log|-1 + tan|-||   5*log|1 + tan |-||   10*x*tan|-|    5*tan |-|*log|1 + tan |-||   5*tan |-|*log|1 + tan|-||   5*tan |-|*log|-1 + tan|-||
 |    5                    \       \2//        \        \2//        \        \2//           \2/          \2/    \        \2//         \2/    \       \2//         \2/    \        \2//
 | -------*x dx = C - ----------------- - ------------------ + ------------------ - ------------ - -------------------------- + ------------------------- + --------------------------
 |    2                          2/x\                2/x\                 2/x\              2/x\                  2/x\                         2/x\                        2/x\       
 | cos (x)               -1 + tan |-|        -1 + tan |-|         -1 + tan |-|      -1 + tan |-|          -1 + tan |-|                 -1 + tan |-|                -1 + tan |-|       
 |                                \2/                 \2/                  \2/               \2/                   \2/                          \2/                         \2/       
/
∫x5cos⁡2(x) dx=C−10xtan⁡(x2)tan⁡2(x2)−1+5log⁡(tan⁡(x2)−1)tan⁡2(x2)tan⁡2(x2)−1−5log⁡(tan⁡(x2)−1)tan⁡2(x2)−1+5log⁡(tan⁡(x2)+1)tan⁡2(x2)tan⁡2(x2)−1−5log⁡(tan⁡(x2)+1)tan⁡2(x2)−1−5log⁡(tan⁡2(x2)+1)tan⁡2(x2)tan⁡2(x2)−1+5log⁡(tan⁡2(x2)+1)tan⁡2(x2)−1\int x \frac{5}{\cos^{2}{\left(x \right)}}\, dx = C - \frac{10 x \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{5 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} - \frac{5 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1} + \frac{5 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 1}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90020
Trazar el gráfico f(x)
Respuesta [src] 
                                                                                      /       2     \        2         /       2     \        2                                        2                       
   10*tan(1/2)              5*(pi*I + log(1 - tan(1/2)))   5*log(1 + tan(1/2))   5*log\1 + tan (1/2)/   5*tan (1/2)*log\1 + tan (1/2)/   5*tan (1/2)*(pi*I + log(1 - tan(1/2)))   5*tan (1/2)*log(1 + tan(1/2))
- -------------- - 5*pi*I - ---------------------------- - ------------------- + -------------------- - ------------------------------ + -------------------------------------- + -----------------------------
          2                                2                          2                     2                           2                                    2                                    2            
  -1 + tan (1/2)                   -1 + tan (1/2)             -1 + tan (1/2)        -1 + tan (1/2)              -1 + tan (1/2)                       -1 + tan (1/2)                       -1 + tan (1/2)
5log⁡(tan⁡2(12)+1)−1+tan⁡2(12)+5log⁡(tan⁡(12)+1)tan⁡2(12)−1+tan⁡2(12)−5log⁡(tan⁡2(12)+1)tan⁡2(12)−1+tan⁡2(12)−5log⁡(tan⁡(12)+1)−1+tan⁡2(12)−10tan⁡(12)−1+tan⁡2(12)−5iπ+5(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−1+tan⁡2(12)−5(log⁡(1−tan⁡(12))+iπ)−1+tan⁡2(12)\frac{5 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{5 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{10 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - 5 i \pi + \frac{5 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right)}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} 
=
= 
                                                                                      /       2     \        2         /       2     \        2                                        2                       
   10*tan(1/2)              5*(pi*I + log(1 - tan(1/2)))   5*log(1 + tan(1/2))   5*log\1 + tan (1/2)/   5*tan (1/2)*log\1 + tan (1/2)/   5*tan (1/2)*(pi*I + log(1 - tan(1/2)))   5*tan (1/2)*log(1 + tan(1/2))
- -------------- - 5*pi*I - ---------------------------- - ------------------- + -------------------- - ------------------------------ + -------------------------------------- + -----------------------------
          2                                2                          2                     2                           2                                    2                                    2            
  -1 + tan (1/2)                   -1 + tan (1/2)             -1 + tan (1/2)        -1 + tan (1/2)              -1 + tan (1/2)                       -1 + tan (1/2)                       -1 + tan (1/2)
5log⁡(tan⁡2(12)+1)−1+tan⁡2(12)+5log⁡(tan⁡(12)+1)tan⁡2(12)−1+tan⁡2(12)−5log⁡(tan⁡2(12)+1)tan⁡2(12)−1+tan⁡2(12)−5log⁡(tan⁡(12)+1)−1+tan⁡2(12)−10tan⁡(12)−1+tan⁡2(12)−5iπ+5(log⁡(1−tan⁡(12))+iπ)tan⁡2(12)−1+tan⁡2(12)−5(log⁡(1−tan⁡(12))+iπ)−1+tan⁡2(12)\frac{5 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} + \frac{5 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \log{\left(\tan^{2}{\left(\frac{1}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \log{\left(\tan{\left(\frac{1}{2} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{10 \tan{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - 5 i \pi + \frac{5 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{2} \right)}}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{5 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right)}{-1 + \tan^{2}{\left(\frac{1}{2} \right)}} 
-10*tan(1/2)/(-1 + tan(1/2)^2) - 5*pi*i - 5*(pi*i + log(1 - tan(1/2)))/(-1 + tan(1/2)^2) - 5*log(1 + tan(1/2))/(-1 + tan(1/2)^2) + 5*log(1 + tan(1/2)^2)/(-1 + tan(1/2)^2) - 5*tan(1/2)^2*log(1 + tan(1/2)^2)/(-1 + tan(1/2)^2) + 5*tan(1/2)^2*(pi*i + log(1 - tan(1/2)))/(-1 + tan(1/2)^2) + 5*tan(1/2)^2*log(1 + tan(1/2))/(-1 + tan(1/2)^2)
Respuesta numérica [src] 
4.70890627134444
4.70890627134444

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

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