Question Number 34255 by math khazana by abdo last updated on 03/May/18
$${find}\:\:{g}\left({x}\right)=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }\:{dt} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{ln}\left(\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} \right)}{{t}^{\mathrm{2}} }{dt}\:. \\ $$