Amazon.com: An Introduction to Probability Theory and Mathematical Statistics (Wiley Series in Probability & Mathematical Statistics): Vijay K. Rohatgi, V. K. Rohatgi: Books) you have the correct result. So you have:
The indefinite integral is given below, so all you need to do is evaluate the definite integral. As for getting the indefinite integral, I could probably get it in under an hour, whereas an inte-killer could probably get it under a minute. But if an inte-killer is indisposed and you have no luck yourself, I could probably manage something ..... (Let's see what the next 24 hours brings).
And I don't think it'd be double posting to post the integral itself (and result) in the calculus forum. That's where you'll must likely find an inte-killer