What is the integral of int ( sin^3(x))dx?

${\cos}^{3} \frac{x}{3} - \cos x + c$
$\int \sin x {\sin}^{2} x \mathrm{dx} = \int \sin x \left(1 - {\cos}^{2} x\right) \mathrm{dx} = \int \sin x \mathrm{dx} - \int \sin x {\cos}^{2} x \mathrm{dx} = - \cos x + {\cos}^{3} \frac{x}{3} + c$