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Resolución de integrales/ x*sqrt/ sin(x)/ sqrt(x)/ sin(x)/(x*sqrt(x))

Integral de sin(x)/(x*sqrt(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |   sin(x)   
 |  ------- dx
 |      ___   
 |  x*\/ x    
 |            
/             
0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sqrt{x} x}\, dx$$ 
Integral(sin(x)/((x*sqrt(x))), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                       /  ___   ___\           
                                           ___   ____  |\/ 2 *\/ x |           
  /                                      \/ 2 *\/ pi *C|-----------|*Gamma(1/4)
 |                                                     |     ____  |           
 |  sin(x)          Gamma(1/4)*sin(x)                  \   \/ pi   /           
 | ------- dx = C - ------------------ + --------------------------------------
 |     ___              ___                           2*Gamma(5/4)             
 | x*\/ x           2*\/ x *Gamma(5/4)                                         
 |                                                                             
/
$$\int \frac{\sin{\left(x \right)}}{\sqrt{x} x}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} - \frac{\sin{\left(x \right)} \Gamma\left(\frac{1}{4}\right)}{2 \sqrt{x} \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                    /  ___ \           
                        ___   ____  |\/ 2  |           
                      \/ 2 *\/ pi *C|------|*Gamma(1/4)
                                    |  ____|           
  Gamma(1/4)*sin(1)                 \\/ pi /           
- ----------------- + ---------------------------------
     2*Gamma(5/4)                2*Gamma(5/4)
$$- \frac{\sin{\left(1 \right)} \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
                                    /  ___ \           
                        ___   ____  |\/ 2  |           
                      \/ 2 *\/ pi *C|------|*Gamma(1/4)
                                    |  ____|           
  Gamma(1/4)*sin(1)                 \\/ pi /           
- ----------------- + ---------------------------------
     2*Gamma(5/4)                2*Gamma(5/4)
$$- \frac{\sin{\left(1 \right)} \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{2 \Gamma\left(\frac{5}{4}\right)}$$ 
-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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