Question Number 31082 by abdo imad last updated on 02/Mar/18
$${calculate}\:{by}\:{two}\:{methods}\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{y}\right)\left(\mathrm{1}+{x}^{\mathrm{2}} {y}\right)} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{lnx}}{\mathrm{1}−{x}^{\mathrm{2}} }{dx}. \\ $$