I must find for which values of $\displaystyle p \in \mathbb{R}$ the following integral converges : $\displaystyle \int_e^{+\infty} \frac{dx}{x\ln^p|x|}$. Mathstud28 already done that (well, something pretty similar) in one of my earlier threads, but I didn't understand a step he did, so I would like a little bit more explanations :

[quote]How about when

Hmm, sorry the quote doesn't work. I copy and past it, but it only shows the first line and all the other is cut, so I quote it by parts :[quote].

Still doesn't work!

Anyway, he was working with $\displaystyle \int_2^{+\infty}\frac{dx}{x\ln^p|x|}$. He said that if $\displaystyle 0<p<1$, then the indefinite integral is equal to $\displaystyle \frac{\ln^{-p+1}(x)}{-p+1}$. This is what I missed to understand. Did he do integration by parts? How could he reach this result? Thanks!!