Question Number 107245 by mnjuly1970 last updated on 09/Aug/20
$$\:\:\:\:\:\:\:\:\clubsuit\:\mathscr{Q}{uestion}\clubsuit \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{W}{hy}\:??? \\ $$$$....\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \sqrt{\frac{\left(\mathrm{2}^{{x}} −\mathrm{1}\right){sin}^{\mathrm{3}} \left({x}\right)}{\left(\mathrm{2}^{{x}} +\mathrm{1}\right)\left({sin}^{\mathrm{3}} \left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)\right)}\:}<\frac{\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\:\:\:....\mathscr{M}.\mathscr{N}.... \\ $$