Question Number 34263 by math khazana by abdo last updated on 03/May/18
$${calculate}\:{I}\:\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}\:\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\frac{{x}^{{n}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{{n}} \right)}{dx}\:{with}\:{n}\:{integr}\:>\mathrm{0} \\ $$