# help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx

• Apr 30th 2013, 11:55 AM
mimophile
help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx
Dear All,
How to solve the following integral (see attachment)?
a,b, are real scalars.
Any help would be much welcome
Thanks
• Apr 30th 2013, 12:02 PM
topsquark
Re: help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx
You wrote it in LaTeX code in the title, why the PDF?

What have you been able to do with this?

-Dan
• Apr 30th 2013, 12:07 PM
mimophile
Re: help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx
PDF because it is easier to read.
I could not find any similar integral in Gradshteyn and Ryzhik's Table of Integrals.
• Apr 30th 2013, 03:26 PM
topsquark
Re: help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx
With a few quick changes and the addition of [tex] tags we get:
$\displaystyle \int_0^{\infty} \frac{e^{-x}}{(x+a)(x+b)} dx$

Have you ever heard of the Laplace transform?

-Dan
• May 1st 2013, 12:54 AM
mimophile
Re: help for solving integral int_0^{infinity} exp(-x) / ((x+a)(x+b)) dx
ok, I got it.
There is no need for Laplace. Simply use partial fraction expansion and expand the integral into a sum of two integral. Each of them can be solved using the exponential integral function Ei.
Thanks