Are you allowed to use software? A certain popular online "calculator" gives a result that's too long for me to type or derive.
First get rid of the complex fractions in the integrand. That gives
Now make the substitution x = ay. This gives (after some work)
This integral looks not too bad, but as I said, it's a picky one. I'll leave the details to WolframAlpha, but it's really not that bad, just tedious.
The procedure is simple enough. First let . After you've simplified that, then let . That gives:
which you can solve by partial fractions. Now backsubstitute to get
As I said, without the physical problem I can't tell you what form of the solution might be the most useful.