Here's what I'm working with:

This does not appear to be a trivial problem, and I'm having trouble figuring out how to approach this. If I try integrating it by parts, I just end up with another integral that's very similar. Tossing this into WolframAlpha shows a *really* complicated u-sub. I've run into situations where WolframAlpha makes things a lot more complicated than they need to be. I'm hoping this is one of those times.

Can anyone give me a hand?