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Resolución de integrales/ (x^2)/ sh(x^2)

Integral de sh(x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2            
  /            
 |             
 |      / 2\   
 |  sinh\x / dx
 |             
/              
1
$$\int\limits_{1}^{2} \sinh{\left(x^{2} \right)}\, dx$$ 
Integral(sinh(x^2), (x, 1, 2))
Respuesta (Indefinida) [src] 
                                              /         pi*I\           
                                     -3*pi*I  |         ----|           
                                     -------  |    ___   4  |           
                         ___   ____     4     |x*\/ 2 *e    |           
  /                  3*\/ 2 *\/ pi *e       *S|-------------|*Gamma(3/4)
 |                                            |      ____   |           
 |     / 2\                                   \    \/ pi    /           
 | sinh\x / dx = C + ---------------------------------------------------
 |                                       8*Gamma(7/4)                   
/
$$\int \sinh{\left(x^{2} \right)}\, dx = C + \frac{3 \sqrt{2} \sqrt{\pi} e^{- \frac{3 i \pi}{4}} S\left(\frac{\sqrt{2} x e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                           /       pi*I\                                       /         pi*I\           
                  -3*pi*I  |       ----|                              -3*pi*I  |         ----|           
                  -------  |  ___   4  |                              -------  |    ___   4  |           
      ___   ____     4     |\/ 2 *e    |                  ___   ____     4     |2*\/ 2 *e    |           
  3*\/ 2 *\/ pi *e       *S|-----------|*Gamma(3/4)   3*\/ 2 *\/ pi *e       *S|-------------|*Gamma(3/4)
                           |     ____  |                                       |      ____   |           
                           \   \/ pi   /                                       \    \/ pi    /           
- ------------------------------------------------- + ---------------------------------------------------
                     8*Gamma(7/4)                                         8*Gamma(7/4)
$$- \frac{3 \sqrt{2} \sqrt{\pi} e^{- \frac{3 i \pi}{4}} S\left(\frac{\sqrt{2} e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sqrt{2} \sqrt{\pi} e^{- \frac{3 i \pi}{4}} S\left(\frac{2 \sqrt{2} e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$ 
=
= 
                           /       pi*I\                                       /         pi*I\           
                  -3*pi*I  |       ----|                              -3*pi*I  |         ----|           
                  -------  |  ___   4  |                              -------  |    ___   4  |           
      ___   ____     4     |\/ 2 *e    |                  ___   ____     4     |2*\/ 2 *e    |           
  3*\/ 2 *\/ pi *e       *S|-----------|*Gamma(3/4)   3*\/ 2 *\/ pi *e       *S|-------------|*Gamma(3/4)
                           |     ____  |                                       |      ____   |           
                           \   \/ pi   /                                       \    \/ pi    /           
- ------------------------------------------------- + ---------------------------------------------------
                     8*Gamma(7/4)                                         8*Gamma(7/4)
$$- \frac{3 \sqrt{2} \sqrt{\pi} e^{- \frac{3 i \pi}{4}} S\left(\frac{\sqrt{2} e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sqrt{2} \sqrt{\pi} e^{- \frac{3 i \pi}{4}} S\left(\frac{2 \sqrt{2} e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$ 
-3*sqrt(2)*sqrt(pi)*exp(-3*pi*i/4)*fresnels(sqrt(2)*exp(pi*i/4)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4)) + 3*sqrt(2)*sqrt(pi)*exp(-3*pi*i/4)*fresnels(2*sqrt(2)*exp(pi*i/4)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))
Respuesta numérica [src] 
7.42735938082503
7.42735938082503

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

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