\(\begin{aligned}
& \int \sin ^3 x \cdot \cos ^3 x d x \\
& \quad=\int \sin ^3 x \cdot \cos x\left(1-\sin ^2 x\right) d x
\end{aligned}\)
Let \(t=\sin x \Rightarrow d t=\cos x \cdot d x\)
\(\begin{aligned}
& \Rightarrow \quad \int t^3 \cdot\left(1-t^2\right) d t=\int\left(t^3-t^5\right) d t \\
& \Rightarrow \quad \frac{t^4}{4}-\frac{t^6}{6}+C=\frac{\sin ^4 x}{4}-\frac{\sin ^6 x}{6}+C
\end{aligned}\)