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Resolución de integrales/ 3/x^2/ sin(3/x^2)*1/

Integral de sin(3/x^2)*1/ dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |     /3 \   
 |  sin|--| dx
 |     | 2|   
 |     \x /   
 |            
/             
0
$$\int\limits_{0}^{1} \sin{\left(\frac{3}{x^{2}} \right)}\, dx$$ 
Integral(sin(3/x^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                         /   ___  \           
                                    /3 \     ___   ____  | \/ 6   |           
  /                 x*Gamma(1/4)*sin|--|   \/ 6 *\/ pi *C|--------|*Gamma(1/4)
 |                                  | 2|                 |  ____  |           
 |    /3 \                          \x /                 \\/ pi *x/           
 | sin|--| dx = C + -------------------- - -----------------------------------
 |    | 2|              4*Gamma(5/4)                   4*Gamma(5/4)           
 |    \x /                                                                    
 |                                                                            
/
$$\int \sin{\left(\frac{3}{x^{2}} \right)}\, dx = C + \frac{x \sin{\left(\frac{3}{x^{2}} \right)} \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)} - \frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6}}{\sqrt{\pi} x}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                                            /  ___ \           
                                                ___   ____  |\/ 6  |           
                                              \/ 6 *\/ pi *C|------|*Gamma(1/4)
                      ___   ____                            |  ____|           
Gamma(1/4)*sin(3)   \/ 6 *\/ pi *Gamma(1/4)                 \\/ pi /           
----------------- + ----------------------- - ---------------------------------
   4*Gamma(5/4)           8*Gamma(5/4)                   4*Gamma(5/4)
$$- \frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sin{\left(3 \right)} \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{6} \sqrt{\pi} \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$ 
=
= 
                                                            /  ___ \           
                                                ___   ____  |\/ 6  |           
                                              \/ 6 *\/ pi *C|------|*Gamma(1/4)
                      ___   ____                            |  ____|           
Gamma(1/4)*sin(3)   \/ 6 *\/ pi *Gamma(1/4)                 \\/ pi /           
----------------- + ----------------------- - ---------------------------------
   4*Gamma(5/4)           8*Gamma(5/4)                   4*Gamma(5/4)
$$- \frac{\sqrt{6} \sqrt{\pi} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sin{\left(3 \right)} \Gamma\left(\frac{1}{4}\right)}{4 \Gamma\left(\frac{5}{4}\right)} + \frac{\sqrt{6} \sqrt{\pi} \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$ 
gamma(1/4)*sin(3)/(4*gamma(5/4)) + sqrt(6)*sqrt(pi)*gamma(1/4)/(8*gamma(5/4)) - sqrt(6)*sqrt(pi)*fresnelc(sqrt(6)/sqrt(pi))*gamma(1/4)/(4*gamma(5/4))
Respuesta numérica [src] 
-0.13995966883563
-0.13995966883563

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

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