# Integral of sqrt(x^2-a^2)exp(-x)

New to the forum, thanks for having me.

I've looked in tables and tried Mathmatica but have not came
up with a formula for the integral over x of

sqrt(x^2-a^2)exp(-x)

If anyone could point me in the right direction I'd be appreciative.
Thanks

$$\int\sqrt{x^2-a^2}e^{-x}dx$$

Integration by parts?

There is a standard formula for integrating $$\int\sqrt{x^2-a^2}dx$$ (that involves logs which might help later with the exponential).

Haven't worked it out myself but that's where i'd start.

Cyosis
Homework Helper
You won't be able to find a primitive.

yeah. wolfram didn't like it when i plugged it in.

Thanks for your help. Seems integration by parts will just require further integrals
of the form (x^2-a^2)^n/2 exp(-x). Maybe I'll just have to integrate numberially for fixed values of a.

The integral from a to infinity can be expressed in terms of a modified Bessel function of the first kind.