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Resolución de integrales/ cosx// x^(3/2)/ cosx/x^(3/2)

Integral de cosx/x^(3/2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo          
  /          
 |           
 |  cos(x)   
 |  ------ dx
 |    3/2    
 |   x       
 |           
/            
2
∫2∞cos⁡(x)x32 dx\int\limits_{2}^{\infty} \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx 
Integral(cos(x)/x^(3/2), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                  /         
 |                  |          
 | cos(x)           | cos(x)   
 | ------ dx = C +  | ------ dx
 |   3/2            |   3/2    
 |  x               |  x       
 |                  |          
/                  /
∫cos⁡(x)x32 dx=C+∫cos⁡(x)x32 dx\int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx = C + \int \frac{\cos{\left(x \right)}}{x^{\frac{3}{2}}}\, dx
Simplificar
Respuesta [src] 
             /              /    ____  /  2   \         \           \
             |              |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
             |              |          |  ____|         |           |
  ___   ____ |Gamma(-1/4)   \          \\/ pi /         /           |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
             | Gamma(3/4)                ____                       |
             \                         \/ pi *Gamma(5/4)            /
---------------------------------------------------------------------
                                  4
2π(Γ(−14)Γ(34)+(cos⁡(2)+2πS(2π))Γ(14)πΓ(54))4\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4} 
=
= 
             /              /    ____  /  2   \         \           \
             |              |2*\/ pi *S|------| + cos(2)|*Gamma(1/4)|
             |              |          |  ____|         |           |
  ___   ____ |Gamma(-1/4)   \          \\/ pi /         /           |
\/ 2 *\/ pi *|----------- + ----------------------------------------|
             | Gamma(3/4)                ____                       |
             \                         \/ pi *Gamma(5/4)            /
---------------------------------------------------------------------
                                  4
2π(Γ(−14)Γ(34)+(cos⁡(2)+2πS(2π))Γ(14)πΓ(54))4\frac{\sqrt{2} \sqrt{\pi} \left(\frac{\Gamma\left(- \frac{1}{4}\right)}{\Gamma\left(\frac{3}{4}\right)} + \frac{\left(\cos{\left(2 \right)} + 2 \sqrt{\pi} S\left(\frac{2}{\sqrt{\pi}}\right)\right) \Gamma\left(\frac{1}{4}\right)}{\sqrt{\pi} \Gamma\left(\frac{5}{4}\right)}\right)}{4} 
sqrt(2)*sqrt(pi)*(gamma(-1/4)/gamma(3/4) + (2*sqrt(pi)*fresnels(2/sqrt(pi)) + cos(2))*gamma(1/4)/(sqrt(pi)*gamma(5/4)))/4

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

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