Condition of an exponent for convergence of an integral

I must find for which values of the following integral converges : . Mathstud28 already done that (well, something pretty similar) in one of my earlier threads, but I didn't understand a step he did, so I would like a little bit more explanations :

[quote]How about when

Hmm, sorry the quote doesn't work. I copy and past it, but it only shows the first line and all the other is cut, so I quote it by parts :[quote].

Still doesn't work!

Anyway, he was working with . He said that if , then the indefinite integral is equal to . This is what I missed to understand. Did he do integration by parts? How could he reach this result? Thanks!!