Here it is
$\displaystyle \int_{0}^{\frac{\pi}{4}} \sin^3(2x)\cos^2(2x)\ where\ the\ sustitution\ is\ u = \cos(2x)$
$\displaystyle \frac{du}{dx} = -\frac{1}{2}\sin(2x)$
which means
$\displaystyle -2\sin^2(2x)u^2.du$
I get stuck here
Here it is
$\displaystyle \int_{0}^{\frac{\pi}{4}} \sin^3(2x)\cos^2(2x)\ where\ the\ sustitution\ is\ u = \cos(2x)$
$\displaystyle \frac{du}{dx} = -\frac{1}{2}\sin(2x)$
which means
$\displaystyle -2\sin^2(2x)u^2.du$
I get stuck here
Just in case it appeals...
This is only an overview - the lower equality relies on the pythag identity.
Balloon Calculus: worked examples from past papers