Improper Integrals: Solving for Integrability of log^a(x)/x^p

[economist1985]

Homework Statement

For what p is f(x)=log^a(x)/x^p integrable from (1,infinity)?

Homework Equations

The Attempt at a Solution

I'm not sure, maybe I can do some sort of inequality so that I can arrive at the comparison theorem for improper integrals.

 

[jbunniii]

It's always integrable from (1,N) for N > 1. Find an expression for that integral, and then try letting $N \rightarrow \infty$. For what $p$ does the limit exist?