Here's what I have so far, but I'm coming up with answers other than the book value. Mind pointing out my error?

$\displaystyle \int sin2xcos2xdx$

Letting $\displaystyle u=sin2x, du=cos2xdx$

$\displaystyle \int udu$

$\displaystyle \frac{u^2}{2}+C$

$\displaystyle \frac{sin^{2}2x}{2}+C$