As part of a larger problem I came across 1/8 the integral of cos^3(2x).

I simplified this to 1/16 the integral of 2(1-sin^2(2x))cosx and then solved with u substitution.

u=sin(2x)

du=2cos(2x)

This came out to [sin^3(2x)]/48.

My teacher tells me that the answer is [sin^3(2x)]/6. I don't see how this is possible. Who is right?