It is asked to study the nature of the improper integral
$$ \displaystyle\int_0^{+\infty} \dfrac{\ln(\arctan(x))}{x^\alpha} dx $$
At $+\infty$, it seems it converges for $\alpha > 1$ since the numerator is bounded and positive for sufficiently large $x$.
What about the problem at $0$.
Thanks for any hints / replies.