Question

Solve the following integral.

$\int se{c}^{2}x{\tan }^{5}xdx$

Short answer

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

Step-by-step solution

Step 1. Given information

An integral is$\int se{c}^{2}x{\tan }^{5}xdx$

Step 2. Explanation

Let $u=\tan x$

$\begin{array}{rcl}\int se{c}^{2}x{\tan }^{5}xdx& =& \int u^{5}du\\ & =& \frac{u^6}{6}+C\\ & =& \frac{{\tan }^{6}x}{6}+C\end{array}$