Here's the integral:
Every method I try to use either hits a dead end or makes the problem more complicated. The only way I've managed to actually complete the integral is using integration by parts and distributing everything all the way out which but that ends up being a hugely complex mess of different terms that I have no way of verifying.
The answer in the back of the book and the answer given by Mathematica is:
However I can't seem to get there. I feel like there must be a way to arrange the completed integral algebraically so that all the complicated terms cancel and you end up with the nice clean answer the book gives, but after an hour of trial and error I haven't found it yet.
Edit: Apologies I did make a typo in this post, it has been corrected but I didn't make that error when computing the problem.
To confirm (for you and myself):