\[\int_{0}^{\pi /2}{\frac{x\sin x\cos x}{{{\cos }^{4}}x+{{\sin }^{4}}x}}\,dx=\] [IIT 1985]

• A.                 0             
• B.                 \[\frac{\pi }{8}\]
• C.                 \[\frac{{{\pi }^{2}}}{8}\]
• D.                 \[\frac{{{\pi }^{2}}}{16}\]