\(\int \frac{\sec^2x}{\sqrt{\tan^2x+4}}dx=\)

\(log|\tan x|+c\) \(log|\tan x+\sec x|+c\) $\log\left|\tan x+\sqrt{\tan^2x+4}\right|+C$ \(log|\tan x-\sqrt{tan^x+4}|+c\)

$\log\left|\tan x+\sqrt{\tan^2x+4}\right|+C$

\(\int \frac{\sec^2xdx}{\sqrt{\tan^2x+4}}\) $=\int\frac{d(\tan x)}{\sqrt{\tan^2x+4}}$ $=\log\left|\tan x+\sqrt{\tan^2x+4}\right|+C$