1. ## Improper integrals, converging

Find all real numbers p such that $\displaystyle \int_2^{\infty}\frac{1}{x(\ln x)^p} dx$ converges

2. Originally Posted by acevipa
Find all real numbers p such that $\displaystyle \int_2^{\infty}\frac{1}{x(\ln x)^p} dx$ converges
Let $\displaystyle u = \ln x$ so your integral becomes

$\displaystyle \int_{\ln 2}^{\infty} \frac{du}{u^p}$.

Look familar?

3. Originally Posted by Danny
Let $\displaystyle u = \ln x$ so your integral becomes

$\displaystyle \int_{\ln 2}^{\infty} \frac{du}{u^p}$.

Look familar?
Where did the x go?

4. Originally Posted by acevipa
Where did the x go?
1/x went with the du. du=1/x.

Also I would prefer first solving the indefinite integral. It's much better approach.