I need to show that an integral from minus infinity to infinity is smaller than infinity. All the expressions that are integrated are positive. What should I do? Can you recommend me some theorems that I can use? Thank you in advance!
As |x| and x^2 are positive, we can write this as,
So checking the convergence of is enough.
We can easily prove that converges.
So converges too.
Now prove the convergence of and it'll be over.
(It looks a little long and I can't think of anything easy at the moment..)