Question Number 108306 by Sayantan chakraborty last updated on 16/Aug/20
$$\mathrm{proof}\:\mathrm{that}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}}{\left({sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}\right)^{\mathrm{2}} }\:{dx}\:=\frac{\mathrm{1}}{\mathrm{6}} \\ $$