$\displaystyle \int sin^{2}xcosx dx $

so using $\displaystyle sin^{2}x = 1 - cos^{2}x $

$\displaystyle \int sin^{2}xcosx dx = \int cosx - cos^{3}x dx $

which is all fine and dandy (i think) but what's the integral of $\displaystyle cos^{3}x $?

is there a better way of doing it?

Also what would be $\displaystyle \int sin^{5}x dx $or $\displaystyle \int cos^{5}x dx $ and $\displaystyle \int cos^{7}x dx$

i guess im looking for a general rule of $\displaystyle \int cos^{n}x dx $ and $\displaystyle \int sin^{n}x dx$

thanks in advance