Integral of xcos^2(2x)

$$ \int x\cos^2\left(2x\right)\differentialD x $$ $$ \int(\frac{x\cos\left(4x\right)}{x}+\frac{x}{2})dx $$ $$ \frac{1}{2}\int x\cos\left(4x\right)\differentialD x+\frac{1}{2}\int x\differentialD x $$ $$ \frac{x\sin\left(4x\right)}{8}+\frac{\cos\left(4x\right)}{32}+\frac{x^2}{4}+C $$ $$ \frac{4x\left(\sin\left(4x\right)+2x\right)+\cos\left(4x\right)}{32}+C $$