Question Number 28541 by abdo imad last updated on 26/Jan/18
$${prove}\:{that}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{sinx}}{{e}^{{ax}} −\mathrm{1}}{dx}=\:\sum_{{p}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{\mathrm{1}+{p}^{\mathrm{2}} {a}^{\mathrm{2}} }\:\:\:\:\:{with}\:{a}>\mathrm{0} \\ $$