Integral de exp(i*x)/(1+x^2) dx
Solución
Respuesta (Indefinida)
[src]
/ /
| |
| I*x | I*x
| e | e
| ------ dx = C + | ------ dx
| 2 | 2
| 1 + x | 1 + x
| |
/ /
$$\int \frac{e^{i x}}{x^{2} + 1}\, dx = C + \int \frac{e^{i x}}{x^{2} + 1}\, dx$$
/ pi \ / pi \ /pi*I \ / pi*I \
- |- -- + I*Shi(1)|*cosh(1) - |- -- - I*Shi(1)|*cosh(1) + I*|---- + Chi(1)|*sinh(1) - I*|- ---- + Chi(1)|*sinh(1)
\ 2 / \ 2 / \ 2 / \ 2 /
$$- \left(- \frac{\pi}{2} + i \operatorname{Shi}{\left(1 \right)}\right) \cosh{\left(1 \right)} - i \left(\operatorname{Chi}\left(1\right) - \frac{i \pi}{2}\right) \sinh{\left(1 \right)} + i \left(\operatorname{Chi}\left(1\right) + \frac{i \pi}{2}\right) \sinh{\left(1 \right)} - \left(- \frac{\pi}{2} - i \operatorname{Shi}{\left(1 \right)}\right) \cosh{\left(1 \right)}$$
=
/ pi \ / pi \ /pi*I \ / pi*I \
- |- -- + I*Shi(1)|*cosh(1) - |- -- - I*Shi(1)|*cosh(1) + I*|---- + Chi(1)|*sinh(1) - I*|- ---- + Chi(1)|*sinh(1)
\ 2 / \ 2 / \ 2 / \ 2 /
$$- \left(- \frac{\pi}{2} + i \operatorname{Shi}{\left(1 \right)}\right) \cosh{\left(1 \right)} - i \left(\operatorname{Chi}\left(1\right) - \frac{i \pi}{2}\right) \sinh{\left(1 \right)} + i \left(\operatorname{Chi}\left(1\right) + \frac{i \pi}{2}\right) \sinh{\left(1 \right)} - \left(- \frac{\pi}{2} - i \operatorname{Shi}{\left(1 \right)}\right) \cosh{\left(1 \right)}$$
-(-pi/2 + i*Shi(1))*cosh(1) - (-pi/2 - i*Shi(1))*cosh(1) + i*(pi*i/2 + Chi(1))*sinh(1) - i*(-pi*i/2 + Chi(1))*sinh(1)
(1.15340239590161 + 0.0j)
(1.15340239590161 + 0.0j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.