In a homework for a standard Calculus I class, we are given this improper integral.
The problem is to prove that it exists. However I am clueless as how to do it. Any hints are appreciated.
My only idea is to apply general convergence criteria for functions or sequences directly.
But this seems hopeless because I can't find a way to calculate the anti-derivative.
Integration by parts only makes this integral even (seemingly) harder and there appears to be no obvious substitution to make.