If $\mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :
- A$\frac{\pi^2}{12}$
- B$\frac{\pi^2}{4}$
- C$\frac{\pi^2}{16}$
- D$\frac{\pi^2}{8}$
✓ Correct answer: C
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