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Resolución de integrales/ x^2-1/ 5cosx/ cosx^2/ 1/(5cosx^2-1)

Integral de 1/(5cosx^2-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  p                 
  -                 
  4                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |       2          
 |  5*cos (x) - 1   
 |                  
/                   
0
∫0p415cos⁡2(x)−1 dx\int\limits_{0}^{\frac{p}{4}} \frac{1}{5 \cos^{2}{\left(x \right)} - 1}\, dx 
Integral(1/(5*cos(x)^2 - 1), (x, 0, p/4))
Respuesta (Indefinida) [src] 
  /                          /        2/x\      /x\\      /        2/x\      /x\\
 |                        log|-1 + tan |-| + tan|-||   log|-1 + tan |-| - tan|-||
 |       1                   \         \2/      \2//      \         \2/      \2//
 | ------------- dx = C - -------------------------- + --------------------------
 |      2                             4                            4             
 | 5*cos (x) - 1                                                                 
 |                                                                               
/
∫15cos⁡2(x)−1 dx=C+log⁡(tan⁡2(x2)−tan⁡(x2)−1)4−log⁡(tan⁡2(x2)+tan⁡(x2)−1)4\int \frac{1}{5 \cos^{2}{\left(x \right)} - 1}\, dx = C + \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} - 1 \right)}}{4}
Simplificar
Respuesta [src] 
     /        2/p\      /p\\      /        2/p\      /p\\
  log|-1 + tan |-| + tan|-||   log|-1 + tan |-| - tan|-||
     \         \8/      \8//      \         \8/      \8//
- -------------------------- + --------------------------
              4                            4
log⁡(tan⁡2(p8)−tan⁡(p8)−1)4−log⁡(tan⁡2(p8)+tan⁡(p8)−1)4\frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} - \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} + \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} 
=
= 
     /        2/p\      /p\\      /        2/p\      /p\\
  log|-1 + tan |-| + tan|-||   log|-1 + tan |-| - tan|-||
     \         \8/      \8//      \         \8/      \8//
- -------------------------- + --------------------------
              4                            4
log⁡(tan⁡2(p8)−tan⁡(p8)−1)4−log⁡(tan⁡2(p8)+tan⁡(p8)−1)4\frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} - \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(\frac{p}{8} \right)} + \tan{\left(\frac{p}{8} \right)} - 1 \right)}}{4} 
-log(-1 + tan(p/8)^2 + tan(p/8))/4 + log(-1 + tan(p/8)^2 - tan(p/8))/4

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

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