Question Number 65400 by mathmax by abdo last updated on 29/Jul/19
$${find}\:{f}\left(\alpha\right)\:=\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\frac{\alpha}{{x}}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:\:\:{with}\:\alpha\geqslant\mathrm{0} \\ $$