# How do you find the integral of sec^5 x dx?

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Deb Share
Apr 11, 2018

$\frac{1}{6} {\sec}^{6} x$

#### Explanation:

first, to simplify, set $u = \sec x$ (or not)

now we have $\int {u}^{5} \mathrm{dx}$

to integrate, bring the power 5 up to 6 and add $\frac{1}{6}$ in front

so we have $\frac{1}{6} {u}^{6}$

so the answer is $\frac{1}{6} {\sec}^{6} x$

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