Question Number 40886 by prof Abdo imad last updated on 28/Jul/18
$${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}{p}+\mathrm{1}} {ln}\left({t}\right)}{{t}^{\mathrm{2}} −\mathrm{1}}{dt}\:=\frac{\pi^{\mathrm{2}} }{\mathrm{24}}\:−\frac{\mathrm{1}}{\mathrm{4}}\sum_{{k}=\mathrm{1}} ^{{p}} \:\frac{\mathrm{1}}{{k}^{\mathrm{2}} } \\ $$