Question Number 125919 by Eric002 last updated on 15/Dec/20
$$\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \frac{{dx}\:{dy}\:{dz}\:{dt}}{\left({cosh}\left({x}\right)+{cosh}\left({y}\right)+{cosh}\left({z}\right)+{cosh}\left({t}\right)\right)^{\mathrm{4}} } \\ $$$$=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)−\mathrm{6}}{\mathrm{12}} \\ $$