Question Number 35586 by abdo mathsup 649 cc last updated on 20/May/18
$${find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left(\alpha\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{from}\:{R}\:. \\ $$