Question Number 91630 by Ar Brandon last updated on 02/May/20
$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$
Commented by Ar Brandon last updated on 02/May/20
$$\mathrm{Hint}:\:\mathrm{Let}\:\mathrm{x}=−\mathrm{u} \\ $$