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Resolución de integrales/ cos^5/ 1/cos/ 1/cos^5x

Integral de 1/cos^5x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |     5      
 |  cos (x)   
 |            
/             
0
∫011cos⁡5(x) dx\int\limits_{0}^{1} \frac{1}{\cos^{5}{\left(x \right)}}\, dx 
Integral(1/(cos(x)^5), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                    
 |                                                                              3      
 |    1             3*log(-1 + sin(x))   3*log(1 + sin(x))     -5*sin(x) + 3*sin (x)   
 | ------- dx = C - ------------------ + ----------------- - --------------------------
 |    5                     16                   16                    2           4   
 | cos (x)                                                   8 - 16*sin (x) + 8*sin (x)
 |                                                                                     
/
∫1cos⁡5(x) dx=C−3sin⁡3(x)−5sin⁡(x)8sin⁡4(x)−16sin⁡2(x)+8−3log⁡(sin⁡(x)−1)16+3log⁡(sin⁡(x)+1)16\int \frac{1}{\cos^{5}{\left(x \right)}}\, dx = C - \frac{3 \sin^{3}{\left(x \right)} - 5 \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{16} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{16}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90025
Trazar el gráfico f(x)
Respuesta [src] 
                                                             3      
  3*log(1 - sin(1))   3*log(1 + sin(1))     -5*sin(1) + 3*sin (1)   
- ----------------- + ----------------- - --------------------------
          16                  16                    2           4   
                                          8 - 16*sin (1) + 8*sin (1)
3log⁡(sin⁡(1)+1)16−3log⁡(1−sin⁡(1))16−−5sin⁡(1)+3sin⁡3(1)−16sin⁡2(1)+8sin⁡4(1)+8\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{- 5 \sin{\left(1 \right)} + 3 \sin^{3}{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8} 
=
= 
                                                             3      
  3*log(1 - sin(1))   3*log(1 + sin(1))     -5*sin(1) + 3*sin (1)   
- ----------------- + ----------------- - --------------------------
          16                  16                    2           4   
                                          8 - 16*sin (1) + 8*sin (1)
3log⁡(sin⁡(1)+1)16−3log⁡(1−sin⁡(1))16−−5sin⁡(1)+3sin⁡3(1)−16sin⁡2(1)+8sin⁡4(1)+8\frac{3 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} - \frac{3 \log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{- 5 \sin{\left(1 \right)} + 3 \sin^{3}{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8} 
-3*log(1 - sin(1))/16 + 3*log(1 + sin(1))/16 - (-5*sin(1) + 3*sin(1)^3)/(8 - 16*sin(1)^2 + 8*sin(1)^4)
Respuesta numérica [src] 
4.00924253004203
4.00924253004203

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

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