Evaluate $\int \cos^{3} x\,dx$.

Explanation

1. 01

   $\cos^{3} x = (1 - \sin^{2} x)\cos x$. Put $t = \sin x$, $dt = \cos x\,dx$.

2. 02

   $\int (1 - t^{2})\,dt = t - \frac{t^{3}}{3} = \sin x - \frac{\sin^{3} x}{3} + C$.