# Homework Help: Determining what values a function converges at

1. Feb 24, 2010

### nigba

1. The problem statement, all variables and given/known data
For what values of p and q does the integral

dx / (x^p * (ln(x))^q) from 1 to infinity

converge?

2. Relevant equations
integration

3. The attempt at a solution
I have no idea how to start figuring this out. I've tried trig substitutions but can't find something that actually makes progress.

2. Feb 24, 2010

### ystael

You don't need to actually evaluate the integral of (find a primitive of) $$x^{-p} \log^{-q} x$$ for generic $$p$$ and $$q$$. Instead, compare the growth behavior of this function to simpler functions whose integrals you know converge or diverge, and try to find critical values of $$p$$ and $$q$$ where the behavior changes.