Evaluate the Integral $\int x \sin x \cos x d x$

Multiple Choice

Evaluate the integral. $\int x \sin x \cos x d x$

A) $- \frac { 1 } { 2 } \cos x \sin x + \frac { 1 } { 2 } x + C$
B) $- \frac { 1 } { 2 } x \sin ^ { 2 } x + \frac { 1 } { 2 } \cos x + C$
C) $\frac { 1 } { 8 } [ \sin 2 x - 2 \cos 2 x ] + C$
D) $\frac { 1 } { 8 } [ \sin 8 x - 8 \cos 8 x ] + C$
E) $\text { none of these }$