Indefinite integral via u-substitution

Let $u = \sin(x)$, so $du = \cos(x)\,dx$. This means the factor $\cos(x)\,dx$ in the original integral can be replaced directly by $du$, while $\sin^3(x)$ becomes $u^3$. The integral transforms into $\int u^3\,du$, which contains only the variable $u$.

Integrating gives $\int u^3\,du = \frac{u^4}{4} + C$. Substituting back $u = \sin(x)$ yields the final answer in terms of $x$.