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Consider the indefinite integral
\[ \int \sin^3{(x)}\ dx \]
\begin{enumerate}
    \item Explain why the substitution $u = \sin{(x)}$ will not work to help evaluate the given integral.
    \item Recall the Fundamental Trigonometric Identity, which states that $\sin^2{(x)} + \cos^2{(x)} = 1$. By observing that $\sin^3{(x)} = \sin^2{(x)}\sin{(x)}$, use this identity to rewrite the integrand as the product of $\sin{(x)}$ and another function.
    \item Explain why the substitution $u = \cos{(x)}$ provides a possible way to evaluate the integral in (b).
    \item Use the work in (a)-(c) above to evaluate the integral $\int \sin^3{(x)}\ dx$.
    \item Use a similar approach to evaluate $\int \cos^3{(x)}\ dx$.
\end{enumerate}

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