Question Number 35218 by abdo.msup.com last updated on 16/May/18
$${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}}{dt}\:=\frac{\pi}{{sin}\left(\pi{a}\right)} \\ $$$${that}\:{we}\:{know}\:\mathrm{0}<{a}<\mathrm{1}\:. \\ $$