Question Number 38460 by maxmathsup by imad last updated on 25/Jun/18
$${let}\:\mid{x}\mid>\mathrm{1}\:{find}\:{the}\:{value}\:{of} \\ $$$${F}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:{ln}\left(\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} \right){dt}\:. \\ $$
Commented by abdo mathsup 649 cc last updated on 05/Jul/18
$${the}\:{Q}\:{is}\:{find}\:{F}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{xt}^{\mathrm{2}} \right){dt}\:{with}\:\mid{x}\mid>\mathrm{1} \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+\mathrm{3}{t}^{\mathrm{2}} \right){dt}. \\ $$$$ \\ $$