Sr Examen
Integral de e^(x^4/4) dx
Solución
Ha introducido
[src]
1 / | | 4 | x | -- | 4 | E dx | / 0
$$\int\limits_{0}^{1} e^{\frac{x^{4}}{4}}\, dx$$
Integral(E^(x^4/4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | -pi*I | 4 ------ / 4 pi*I\ | x ___ 4 | x *e | | -- \/ 2 *e *Gamma(1/4)*lowergamma|1/4, --------| | 4 \ 4 / | E dx = C + -------------------------------------------------- | 16*Gamma(5/4) /
$$\int e^{\frac{x^{4}}{4}}\, dx = C + \frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{x^{4} e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
Gráfica
Respuesta
[src]
-pi*I
------ / pi*I\
___ 4 | e |
\/ 2 *e *Gamma(1/4)*lowergamma|1/4, -----|
\ 4 /
-----------------------------------------------
16*Gamma(5/4)
$$\frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
=
=
-pi*I
------ / pi*I\
___ 4 | e |
\/ 2 *e *Gamma(1/4)*lowergamma|1/4, -----|
\ 4 /
-----------------------------------------------
16*Gamma(5/4)
$$\frac{\sqrt{2} e^{- \frac{i \pi}{4}} \Gamma\left(\frac{1}{4}\right) \gamma\left(\frac{1}{4}, \frac{e^{i \pi}}{4}\right)}{16 \Gamma\left(\frac{5}{4}\right)}$$
sqrt(2)*exp(-pi*i/4)*gamma(1/4)*lowergamma(1/4, exp_polar(pi*i)/4)/(16*gamma(5/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.