Question Number 151066 by qaz last updated on 18/Aug/21
$$\mathrm{Calculate}\:\:::\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{arctan}\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{2}}\right)+\mathrm{arctan}\left(\frac{\mathrm{cos}\:\mathrm{3x}+\mathrm{15cos}\:\mathrm{x}}{\mathrm{8}}\right)\right)\mathrm{dx} \\ $$$$=\frac{\pi^{\mathrm{2}} }{\mathrm{4}}−\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$