Integrate the function: $\frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}}$

(N/A) Let $\tan x = t$.
Then,$\sec ^{2} x \, dx = dt$.
Substituting these into the integral,we get:
$\int \frac{\sec ^{2} x}{\sqrt{\tan ^{2} x+4}} \, dx = \int \frac{dt}{\sqrt{t^{2} + 2^{2}}}$.
Using the standard integral formula $\int \frac{dx}{\sqrt{x^{2} + a^{2}}} = \log |x + \sqrt{x^{2} + a^{2}}| + C$,we have:
$= \log |t + \sqrt{t^{2} + 4}| + C$.
Substituting back $t = \tan x$,the final result is:
$= \log |\tan x + \sqrt{\tan^{2} x + 4}| + C$,where $C$ is an arbitrary constant.