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Resolución de integrales/ (x-1)/ sin(pi*x)/ (sin(pi*x))^2/(x-1)^(5/2)

Integral de (sin(pi*x))^2/(x-1)^(5/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo              
  /              
 |               
 |     2         
 |  sin (pi*x)   
 |  ---------- dx
 |         5/2   
 |  (x - 1)      
 |               
/                
2
$$\int\limits_{2}^{\infty} \frac{\sin^{2}{\left(\pi x \right)}}{\left(x - 1\right)^{\frac{5}{2}}}\, dx$$ 
Integral(sin(pi*x)^2/(x - 1)^(5/2), (x, 2, oo))
Respuesta [src] 
  2 /8*C(2)*Gamma(-1/4)   Gamma(1/4)*Gamma(3/4)\
pi *|------------------ + ---------------------|
    \   3*Gamma(3/4)      Gamma(5/4)*Gamma(7/4)/
------------------------------------------------
                       4
$$\frac{\pi^{2} \left(\frac{8 C\left(2\right) \Gamma\left(- \frac{1}{4}\right)}{3 \Gamma\left(\frac{3}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right)}{\Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)}\right)}{4}$$ 
=
= 
  2 /8*C(2)*Gamma(-1/4)   Gamma(1/4)*Gamma(3/4)\
pi *|------------------ + ---------------------|
    \   3*Gamma(3/4)      Gamma(5/4)*Gamma(7/4)/
------------------------------------------------
                       4
$$\frac{\pi^{2} \left(\frac{8 C\left(2\right) \Gamma\left(- \frac{1}{4}\right)}{3 \Gamma\left(\frac{3}{4}\right)} + \frac{\Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right)}{\Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)}\right)}{4}$$ 
pi^2*(8*fresnelc(2)*gamma(-1/4)/(3*gamma(3/4)) + gamma(1/4)*gamma(3/4)/(gamma(5/4)*gamma(7/4)))/4

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

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