I'm supposed to integrate 8*cos^3(2x)*sin(2x).

I'm whittling it down. I factor out a cosine and use the property cos^2(2x)=1-sin^2(2x).

This gives me the integral of 8*((1-sin^2(2x))*cos(2x)*sin(2x)).

Here I substitute u=sin(2x) and du=2cos(2x)

So I have 1/2 the integral of (1-u^2)*u*du

I suspect that by now I've messed it up. The final answer I SHOULD get is -(cos(2x)^4) What's going on?

Thanks in advance!