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Resolución de integrales/ (x^3)/ sin(x)/ sin(x)/√(x^3)

Integral de sin(x)/√(x^3) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |   sin(x)   
 |  ------- dx
 |     ____   
 |    /  3    
 |  \/  x     
 |            
/             
0
∫01sin⁡(x)x3 dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sqrt{x^{3}}}\, dx 
Integral(sin(x)/sqrt(x^3), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                   /          
 |                   |           
 |  sin(x)           |  sin(x)   
 | ------- dx = C +  | ------- dx
 |    ____           |    ____   
 |   /  3            |   /  3    
 | \/  x             | \/  x     
 |                   |           
/                   /
∫sin⁡(x)x3 dx=C+∫sin⁡(x)x3 dx\int \frac{\sin{\left(x \right)}}{\sqrt{x^{3}}}\, dx = C + \int \frac{\sin{\left(x \right)}}{\sqrt{x^{3}}}\, dx
Simplificar
Respuesta [src] 
                                    /  ___ \           
                        ___   ____  |\/ 2  |           
                      \/ 2 *\/ pi *C|------|*Gamma(1/4)
                                    |  ____|           
  Gamma(1/4)*sin(1)                 \\/ pi /           
- ----------------- + ---------------------------------
     2*Gamma(5/4)                2*Gamma(5/4)
−sin⁡(1)Γ(14)2Γ(54)+2πC(2π)Γ(14)2Γ(54)- \frac{\sin{\left(1 \right)} \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} 
=
= 
                                    /  ___ \           
                        ___   ____  |\/ 2  |           
                      \/ 2 *\/ pi *C|------|*Gamma(1/4)
                                    |  ____|           
  Gamma(1/4)*sin(1)                 \\/ pi /           
- ----------------- + ---------------------------------
     2*Gamma(5/4)                2*Gamma(5/4)
−sin⁡(1)Γ(14)2Γ(54)+2πC(2π)Γ(14)2Γ(54)- \frac{\sin{\left(1 \right)} \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} 
-gamma(1/4)*sin(1)/(2*gamma(5/4)) + sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)/sqrt(pi))*gamma(1/4)/(2*gamma(5/4))
Respuesta numérica [src] 
1.93515498145471
1.93515498145471

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

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