Question Number 33297 by abdo imad last updated on 14/Apr/18
$${find}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{ln}\left(\mathrm{1}+{x}\:{sin}\theta\right){d}\theta\:\:\:{with}\:\:\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}{sin}\theta\right){d}\theta \\ $$