(1) Evaluate $\displaystyle \int{{\cos}^{{5}}{x}}{\left.{d}{x}\right.}$.

Hint: Express $\displaystyle {{\cos}^{{4}}{x}}$ in terms of $\displaystyle {\sin{{x}}}$. Then use the substitution $\displaystyle {u}={\sin{{x}}}$. Back substitute to write your soluton in terms of $\displaystyle {x}$.

solution $\displaystyle =$ $\displaystyle +{C}$
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(2) Evaluate $\displaystyle \int{{\cos}^{{2}}{x}}{\left.{d}{x}\right.}$.

Hint: Use the half-angle identity $\displaystyle {{\cos}^{{2}}{x}}=\frac{{1}}{{2}}{\left({1}+{\cos{{2}}}{x}\right)}$.

solution $\displaystyle =$ $\displaystyle +{C}$
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