Question Number 76967 by Maclaurin Stickker last updated on 01/Jan/20
$$\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left(\sqrt{{x}}\right)}{{e}^{\mathrm{2}\pi\sqrt{{x}}} −\mathrm{1}}{dx}+\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{{n}}{{e}^{{n}\:} }=? \\ $$