I have come across the following problem in a calculus textbook:
We are asked to find the values of $ \beta \in \mathbb{R} $ for which the improper integral
$$ \int_{1}^{\infty}x^2 \cos({x^\beta})dx $$
converges.
In fact, I have no idea at all where to start on this it doesn't look like something familiar at all. All help is appreciated.