# How do I evaluate the indefinite integral inttan^2(x)dx ?

Jul 30, 2014

$= \tan x - x + c$, where $c$ is a constant

Using Trigonometric Identity, which is

${\sec}^{2} x - {\tan}^{2} x = 1$

${\tan}^{2} x = {\sec}^{2} x - 1$

Using this Trigonometric Identity in integration,

$= \int \left({\sec}^{2} x - 1\right) \mathrm{dx}$

$= \int {\sec}^{2} x \mathrm{dx} - \int \mathrm{dx}$

$= \tan x - x + c$, where $c$ is a constant