it's quite easy, first note that for the last integral put so the last challenge is to compute which comes from the fact that
eventually, your integral equals
He used the Gamma function's reflection formula.
Gamma function - Wikipedia, the free encyclopedia
Take a look here , the integral can be generalized to that has a new lower and upper limit :
http://www.mathhelpforum.com/math-he...egral-bee.html
Please read the criteria for posting in the Challenge subforum: http://www.mathhelpforum.com/math-he...ion-forum.html