Question Number 112369 by mathdave last updated on 07/Sep/20
$${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{tanh}{x}}{{x}^{\mathrm{3}} }−\frac{\mathrm{sech}^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} }\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\zeta\left(\mathrm{3}\right) \\ $$$${where}\:\zeta\left(\mathrm{3}\right)={apery}'{s}\:{constant} \\ $$