solving $\int \cos^2(2x)\sin(2x)\,dx$ 
$$\int \cos^2(2x)\sin(2x)\,dx$$

I have tried $\int \cos^2(2x)\sin(2x)\,dx=\int (1-\sin^2(2x))\sin(2x)\,dx$
And $\int \cos^2(2x)\sin(2x)\,dx=\int (\cos^2(2x))2\cos x\sin x\, dx$
But no substitution seems to work. 

$$\int  \cos ^{ 2 } (2x)sin(2x)dx=-\frac { 1 }{ 2 } \int { \cos ^{ 2 }{ \left( 2x \right) d\left( \cos { \left( 2x \right)  }  \right)  }  } =-\frac { \cos ^{ 3 }{ \left( 2x \right)  }  }{ 6 } +C$$
substitution here is $u=\cos { \left( 2x \right)  } $
