Sr Examen
Integral de COSH(x^2) dx
Solución
Ha introducido
[src]
1/2 / | | / 2\ | cosh\x / dx | / 0
$$\int\limits_{0}^{\frac{1}{2}} \cosh{\left(x^{2} \right)}\, dx$$
Integral(cosh(x^2), (x, 0, 1/2))
Respuesta (Indefinida)
[src]
/ pi*I\
-pi*I | ----|
------ | ___ 4 |
___ ____ 4 |x*\/ 2 *e |
/ \/ 2 *\/ pi *e *C|-------------|*Gamma(1/4)
| | ____ |
| / 2\ \ \/ pi /
| cosh\x / dx = C + ------------------------------------------------
| 8*Gamma(5/4)
/
$$\int \cosh{\left(x^{2} \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{\sqrt{2} x e^{\frac{i \pi}{4}}}{\sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
/ pi*I\
-pi*I | ----|
------ | ___ 4 |
___ ____ 4 |\/ 2 *e |
\/ 2 *\/ pi *e *C|-----------|*Gamma(1/4)
| ____ |
\ 2*\/ pi /
----------------------------------------------
8*Gamma(5/4)
$$\frac{\sqrt{2} \sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{\sqrt{2} e^{\frac{i \pi}{4}}}{2 \sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
=
=
/ pi*I\
-pi*I | ----|
------ | ___ 4 |
___ ____ 4 |\/ 2 *e |
\/ 2 *\/ pi *e *C|-----------|*Gamma(1/4)
| ____ |
\ 2*\/ pi /
----------------------------------------------
8*Gamma(5/4)
$$\frac{\sqrt{2} \sqrt{\pi} e^{- \frac{i \pi}{4}} C\left(\frac{\sqrt{2} e^{\frac{i \pi}{4}}}{2 \sqrt{\pi}}\right) \Gamma\left(\frac{1}{4}\right)}{8 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(2)*sqrt(pi)*exp(-pi*i/4)*fresnelc(sqrt(2)*exp(pi*i/4)/(2*sqrt(pi)))*gamma(1/4)/(8*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.