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Chapter 5: Q 42. (page 452)

Solve the following integral.
$\int s e c^{2} x \tan^{5} x d x$

Short Answer

Expert verified

Answer is $\frac{\tan^{6} x}{6} + C$

Step by step solution

01

Step 1. Given information

An integral is $\int s e c^{2} x \tan^{5} x d x$

02

Step 2. Explanation

Let $u = \tan x$

$\begin{array}{rcl} \int s e c^{2} x \tan^{5} x d x & = & \int u^{5} d u \\ = & \frac{u^{6}}{6} + C \\ = & \frac{\tan^{6} x}{6} + C \end{array}$

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