Definately having some problems with these.

Question is evalueate the indefinate integral

$\displaystyle \int {\sin ^3 } x\_\cos x\_dx$

I get as far as this, I seem to be having issues with these.

$\displaystyle \int {\sin ^2 } x\_\sin x\_\cos x\_dx$

$\displaystyle \int {(1 - \cos ^2 } x)\sin x\cos x\_dx$

$\displaystyle u = \cos x $ $\displaystyle du = - \sin x$

The answer is:

$\displaystyle \frac{1}{4}\sin ^4 x + C

$