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Resolución de integrales/ cos^3/ sin^2/ 1/(sin^2(x)cos^3(x))

Integral de 1/(sin^2(x)cos^3(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     2       3      
 |  sin (x)*cos (x)   
 |                    
/                     
2
∫2∞1sin⁡2(x)cos⁡3(x) dx\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx 
Integral(1/(sin(x)^2*cos(x)^3), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                                                                                       
 |                                                                                 2      
 |        1                 3*log(-1 + sin(x))   3*log(1 + sin(x))       -2 + 3*sin (x)   
 | --------------- dx = C - ------------------ + ----------------- - ---------------------
 |    2       3                     4                    4                            3   
 | sin (x)*cos (x)                                                   -2*sin(x) + 2*sin (x)
 |                                                                                        
/
∫1sin⁡2(x)cos⁡3(x) dx=C−3sin⁡2(x)−22sin⁡3(x)−2sin⁡(x)−3log⁡(sin⁡(x)−1)4+3log⁡(sin⁡(x)+1)4\int \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx = C - \frac{3 \sin^{2}{\left(x \right)} - 2}{2 \sin^{3}{\left(x \right)} - 2 \sin{\left(x \right)}} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{4}
Simplificar
Respuesta [src] 
 oo                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     3       2      
 |  cos (x)*sin (x)   
 |                    
/                     
2
∫2∞1sin⁡2(x)cos⁡3(x) dx\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx 
=
= 
 oo                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     3       2      
 |  cos (x)*sin (x)   
 |                    
/                     
2
∫2∞1sin⁡2(x)cos⁡3(x) dx\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx 
Integral(1/(cos(x)^3*sin(x)^2), (x, 2, oo))

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

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