Sr Examen
Integral de exp(i*x)/(x^2+5^2)^2 dx
Solución
Ha introducido
[src]
oo / | | I*x | e | ---------- dx | 2 | / 2 \ | \x + 25/ | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{e^{i x}}{\left(x^{2} + 25\right)^{2}}\, dx$$
Integral(exp(i*x)/(x^2 + 25)^2, (x, -oo, oo))
Respuesta
[src]
/ | -pi*I\ / | pi*I\
__1, 3 |1/2, 0, -1 | 4*e | __1, 3 |1/2, 0, -1 | 4*e |
I*/__ | | --------| I*/__ | | -------|
\_|3, 1 \ 0 | 25 / \_|3, 1 \ 0 | 25 /
- ------------------------------------ + -----------------------------------
____ ____
625*\/ pi 625*\/ pi
$$- \frac{i {G_{3, 1}^{1, 3}\left(\begin{matrix} \frac{1}{2}, 0, -1 & \\0 & \end{matrix} \middle| {\frac{4 e^{- i \pi}}{25}} \right)}}{625 \sqrt{\pi}} + \frac{i {G_{3, 1}^{1, 3}\left(\begin{matrix} \frac{1}{2}, 0, -1 & \\0 & \end{matrix} \middle| {\frac{4 e^{i \pi}}{25}} \right)}}{625 \sqrt{\pi}}$$
=
=
/ | -pi*I\ / | pi*I\
__1, 3 |1/2, 0, -1 | 4*e | __1, 3 |1/2, 0, -1 | 4*e |
I*/__ | | --------| I*/__ | | -------|
\_|3, 1 \ 0 | 25 / \_|3, 1 \ 0 | 25 /
- ------------------------------------ + -----------------------------------
____ ____
625*\/ pi 625*\/ pi
$$- \frac{i {G_{3, 1}^{1, 3}\left(\begin{matrix} \frac{1}{2}, 0, -1 & \\0 & \end{matrix} \middle| {\frac{4 e^{- i \pi}}{25}} \right)}}{625 \sqrt{\pi}} + \frac{i {G_{3, 1}^{1, 3}\left(\begin{matrix} \frac{1}{2}, 0, -1 & \\0 & \end{matrix} \middle| {\frac{4 e^{i \pi}}{25}} \right)}}{625 \sqrt{\pi}}$$
-i*meijerg(((1/2, 0, -1), ()), ((0,), ()), 4*exp_polar(-pi*i)/25)/(625*sqrt(pi)) + i*meijerg(((1/2, 0, -1), ()), ((0,), ()), 4*exp_polar(pi*i)/25)/(625*sqrt(pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.