For what values of p makes the integral converge?

Note that this assume ; if that were the case, we'd end up with a logarithm as the antiderivative, and it's easy to show that in that case the integral diverges.



We have two cases remaining. If , then the numerator is of degree larger than 0, and as we have .

If , then the degree of the numerator will be negative, which would mean the numerator approaches 0 as , leaving us with just . So the integral only converges for .