# Improperly integrable

1. Nov 1, 2009

### economist1985

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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.

2. Nov 1, 2009

### 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?