Integral converges/diverges Question:
$$p \in \Bbb R  \int _0 ^\infty \frac {\sin x}{x^p}dx$$
For what values of p does this integral converge/diverge?
Thoughts
We've tried using Dirichlet criteria and bounding it from below, after splitting it from $[0,1]$ and $[1.\infty]$ There seems to be some kind of trick we are probably missing.

The sharp border is $p \geq 1$. for $p = 1$ you have
$${\rm sinc}(x) = \frac{\sin x}x$$
About which you can show
$$\int_a^b {\rm sinc}(x)\ dx \leq C < \infty \qquad \forall a,b \in \mathbb R$$
