Question Number 91982 by M±th+et+s last updated on 04/May/20
$${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {csc}\left({x}\right)\:{tan}^{−\mathrm{1}} \left({sin}\left({x}\right)\right)\:{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$