Question Number 112522 by mathdave last updated on 08/Sep/20
$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} \mathrm{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−{x}^{\mathrm{4}} }{dx}=\frac{\mathrm{7}}{\mathrm{8}}\zeta\left(\mathrm{3}\right)−\frac{\pi^{\mathrm{3}} }{\mathrm{32}} \\ $$