Why $\ln (1/x) \in L^p ( (0, 1] )$ for $1\leq p < \infty$?
From case of $p=1$ it's easy but case of $1<p$
I tried to use the change of variable $log(x)=e^u$ and convert $$ \int_0^1 |\log (1/x)|^p \, dx $$ into $$ \int_{-\infty}^0 |u|^p ue^u \, du. $$
but i cant continue the excercise