This question appeared on a Mathematics PhD Preliminary Examination - Real Analysis section.
Let $Q=\{{0 $$x^ay^b \int_{0}^{\infty}\frac{1}{(x+t)(y^2+t^2)}dt$$ bounded on $Q$? I've tried integrating by parts but it seemed to make the problem more complicated. Ended up needing to further integrate $ln (x+t)$ or $arctan \frac{t}{y}$. Is the right first step to, instead, bring the $x^ay^b$ into the integral to try to bound the overall integrand? If someone could give the right approach for such problems, or just a good starting point, that would be great. Thanks.