Evaluate the Integral $\int x \sin 5 x \cos 5 x d x$

Multiple Choice

Evaluate the integral. $\int x \sin 5 x \cos 5 x d x$

A) $-\frac{1}{12} x \sin ^{2} x+\frac{1}{12} \cos x+C$
B) $\frac{1}{288}[\sin 288 x-288 \cos 288 x]+C$
C) $-\frac{1}{12} \cos x \sin x+\frac{1}{12} x+C$
D) $\frac{1}{288}[\sin 12 x-12 \cos 12 x]+C$
E) $\text { none of these }$