Hi

So this is something that came from a problem we did in probability. I hope it's a correct result, since I modified it a bit.

So I know the probabilitistic way to prove it. If you can find, then do it (but you'd have to know where you're going).

Otherwise, I don't know if there is a calculus approach lol, hence this thread.

Find $\displaystyle \int_{\mathbb{R}} \frac{1}{(1+u^2)^k} ~du$

for any positive integer k.

Answer should be :

Spoiler: