Prove for that This is actually a direct application of Beta function.
This is also a really nice problem, the first time I saw it, I attempted to compute both values of the integrals.
No matter what is. Let & Assume that compute
I recently posted (in another forum) a proof for that also could be another nice problem to do. (You can see its solution here. It's written in spanish, but I think you can get the main ideas.)
Compute When I saw this problem, I developed a solution which involves double integration & series application. (If someone is interested, see my solution here.)
Evaluate This one I love it! It's easy and nice!
I have many others problems, but I don't remember them now, but try these ones.