Question Number 31465 by abdo imad last updated on 08/Mar/18
$${find}\:\:{F}\left(\alpha\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:\alpha\:\in\:{R}−\left\{\mathrm{1},−\mathrm{1}\right\} \\ $$