Answer
$\int$sin$^{3}$x cosx dx = $\frac{1}{4}$sin$^{4}$x +c where c is an arbitrary constant
Work Step by Step
To solve this integral, we will attempt to find the a derivative and antiderivative pair.
$\frac{d}{dx}$sin$^{4}$x =4sin$^{3}$x $\times$ $\frac{d}{dx}$(sinx)
=4sin$^{3}$x cosx
Therefore, $\int$sin$^{3}$x cosx dx = $\frac{1}{4}\int$4 sin$^{3}$x cosx dx
=$\frac{1}{4}$sin$^{4}$x +c where c is an arbitrary constant
