Well, actually, there's a problem, as for the convergence of the integral. But I'm a bit tired to study it ><=
Then du= dy
Is this right so far? Is there some reason why should be one? Could somebody show me how to integrate this by parts? (I know I should be able to do it but I am really struggling).
Make the substitution , assuming that . Otherwise, you'd have to change the boundaries of the integral, and it makes it more complicated.
Then, you'll get something like
For this integral, see the Gamma function : Gamma function - Wikipedia, the free encyclopedia and it should be okay !
I hope that what I babbled will help you in your process. Anyway, it's nice to see your working