Again, improper integrals involving $\ln(1+x^2)$ How can I check for which values of $\alpha $ this integral $$\int_{0}^{\infty} \frac{\ln(1+x^2)}{x^\alpha}\,dx $$ converges? 
I managed to do this in $0$ because I know $\ln(1+x)\sim x$ near 0. 
I have no idea how to do this in $\infty$ where nothing is known about $\ln(x)$ .
Will someone help me ? 
Thanks! 

HINT 
I suggest you develop $\log(1+x^2)$ as an infinite series (Taylor); divide each term by $x^a$, compute the anti-derivative and look where and when arrive the problems when you compute the integral between zero and infinity.
