# How do I evaluate the indefinite integral intsec^2(x)*tan(x)dx ?

Jun 8, 2018

The answer is $= \frac{1}{2} {\sec}^{2} x + C$

#### Explanation:

Perform this integral by substitution

Let $u = {\sec}^{2} x$, $\implies$, $\mathrm{du} = 2 {\sec}^{2} x \tan x \mathrm{dx}$

Therefore, the integral is

$I = \int {\sec}^{2} x \tan x \mathrm{dx} = \frac{1}{2} \int \mathrm{du}$

$= \frac{1}{2} u$

$= \frac{1}{2} {\sec}^{2} x + C$