Answer
\[\frac{{{{\sin }^4}x}}{4} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{{\sin }^3}x\cos xdx} \hfill \\
\hfill \\
set \hfill \\
u = \sin \,x\,\,\,\,\,\,then\,\,\,\,\,du = \cos xdx\, \hfill \\
\hfill \\
{\text{Therefore}}{\text{,}} \hfill \\
\hfill \\
\int_{}^{} {{u^3}\,du} \hfill \\
\hfill \\
{\text{integrating}} \hfill \\
\hfill \\
= \frac{{{u^4}}}{4} + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,\,u = \sin x \hfill \\
\hfill \\
\frac{{{{\sin }^4}x}}{4} + C \hfill \\
\end{gathered} \]
