Hi I'm doing a dynamics problem, To get it into the form wanted I've reduced the problem to showing that

Apologies, the above latex code renders fine on my machine but it looks like the forum doesn't support it

It's meant to say

\int_{0}^{\pi/2} \cos^2 x \sin^8 x dx = \frac{1}{9} \int_{0}^{\pi/2} \cos^{10} x dx

Is there any obvious quick way of doing this, or a hint would be nice, I've thought of integrating it by parts but I cant quite see a nice way of splitting it.