# Integrate: tan^-1 (sec x+tan x) dx : x belong [-pi/2 ,pi/2 )

Solution:

$I= \int \tan^{-1}(\sec x +\tan x)dx\\ \\ \Rightarrow \hspace{1cm}I=\int \tan^{-1}(\tan (\frac{\pi}{4}+\frac{x}{2}))dx\\ \\ \Rightarrow \hspace{1cm}I=\int (\frac{\pi}{4}+\frac{x}{2})dx \\ \\ \Rightarrow \hspace{1cm}I=\frac{\pi}{4}x+\frac{x^{2}}{4}+c$

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