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Resolución de integrales/ (x^3)/ sinx/sqrt(x^3)

Integral de sinx/sqrt(x^3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

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

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

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