Question Number 125233 by mathmax by abdo last updated on 09/Dec/20
$$\mathrm{calculate}\:\mathrm{u}_{\mathrm{nm}} =\int_{\mathrm{0}} ^{\infty} \mathrm{e}^{−\mathrm{nx}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{mx}} \right)\mathrm{dx} \\ $$$$\mathrm{find}\:\sum_{\mathrm{n}\geqslant\mathrm{0}\:\mathrm{and}\:\mathrm{m}\geqslant\mathrm{0}} \:\:\mathrm{u}_{\mathrm{nm}} \\ $$