Solve $\int sin(x) cos^2(x) dx$

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Solve the following integral: \begin{equation*}I = \int sin(x) cos^2(x) dx\end{equation*}

even

1. Transform the integrand by making the substitution $u = cos(x), du = -sin(x) dx$.

\begin{equation*}I = -\int u^2 du\end{equation*}

2. Use the formula for $\int x^n dx$

\begin{equation*} = - \frac{u^3}{3} + constant\end{equation*}

3. Substitute back $u$ in terms of $x$.

\begin{equation*} = -\frac{1}{3}cos^3(x)+constant\end{equation*}