# Thread: Non-Trivial Definite Integral with Exponential

1. ## Non-Trivial Definite Integral with Exponential

Hi,

Does someone how to solve the integral

Int^(+ Infinity)_(- Infinity) dx (x e^( -x/2) ) / (1 + a x^2 e^(- x) )

a is an arbitrary constant.
The integral runs from - Infinity to + Infinity.

I tried solving it with substitution, but it doesnt seem to work.

Regards
Abdullah

2. Originally Posted by abdullah
Hi,

Does someone how to solve the integral

Int^(+ Infinity)_(- Infinity) dx (x e^( -x/2) ) / (1 + a x^2 e^(- x) )

a is an arbitrary constant.
The integral runs from - Infinity to + Infinity.

I tried solving it with substitution, but it doesnt seem to work.

Regards
Abdullah
There is no closed form for the indefinite integral, so I'd say this one is ripe for contour integration.

-Dan