# Evaluate the integral. {eq}\int \cos^2 x \tan^3 x \, \mathrm{d}x {/eq}

## Question:

Evaluate the integral.

{eq}\int \cos^2 x \tan^3 x \, \mathrm{d}x {/eq}

## U-Substitution:

U-substitution is used to evaluate integrals by replacing an appropriate sub-function with {eq}u {/eq}. The derivative of the sub-function must also be taken as it will be utilized as the value of {eq}\mathrm{d}u {/eq}.

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We first need to simplify the given integral by implementing the trigonometric identities {eq}\displaystyle \tan(x) = \frac{\sin(x)}{\cos(x)} {/eq}...