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Question Number 91982 by  M±th+et+s last updated on 04/May/20
show that   ∫_0 ^(π/2) csc(x) tan^(−1) (sin(x)) dx=(π/2)ln(1+(√2))
$${show}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {csc}\left({x}\right)\:{tan}^{−\mathrm{1}} \left({sin}\left({x}\right)\right)\:{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$

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