If $$I=\int_{0}^{\frac{\pi}{2}}\frac{\sin^{\frac{3}{2}} x}{\sin^{\frac{3}{2}} x+ \cos^{\frac{3}{2} x}}dx$$, then $$\int_{0}^{21}\frac{x\sin x \cos x}{\sin^{4} x+\cos^{4} x}dx$$ equals :

A

$$\frac{\pi^{2}}{12}$$

B

$$\frac{\pi^{2}}{4}$$

C

$$\frac{\pi^{2}}{16}$$

D

$$\frac{\pi^{2}}{8}$$