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Integral de exp(i*x)/(1+x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 oo          
  /          
 |           
 |    I*x    
 |   e       
 |  ------ dx
 |       2   
 |  1 + x    
 |           
/            
-oo          
$$\int\limits_{-\infty}^{\infty} \frac{e^{i x}}{x^{2} + 1}\, dx$$
Integral(exp(i*x)/(1 + x^2), (x, -oo, oo))
Respuesta (Indefinida) [src]
  /                  /         
 |                  |          
 |   I*x            |   I*x    
 |  e               |  e       
 | ------ dx = C +  | ------ dx
 |      2           |      2   
 | 1 + x            | 1 + x    
 |                  |          
/                  /           
$$\int \frac{e^{i x}}{x^{2} + 1}\, dx = C + \int \frac{e^{i x}}{x^{2} + 1}\, dx$$
Respuesta [src]
  /  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)
Respuesta numérica [src]
(1.15340239590161 + 0.0j)
(1.15340239590161 + 0.0j)

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