If \(I=\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} d x\), then \(\int_{0}^{\frac{\pi}{2}} \frac{x \sin x \cos x}{\sin ^{4} x+\cos ^{4} x} d x\) equals:
1
\(\frac{\pi^{2}}{16}\)
2
\(\frac{\pi^{2}}{4}\)
3
\(\frac{\pi^{2}}{8}\)
4
\(\frac{\pi^{2}}{12}\)