Integrate the functions`(sec^2x)/(sqrt(tan^2x+4))`

Explanation

To solve the integral \(\int \frac{\sec^2 x}{\sqrt{\tan^2 x + 4}} \, dx\), we will use the substitution method. Here’s a step-by-step solution:

### Step 1: Substitution
Let \( t = \tan x \). Then, the derivative of \( t \) with respect to \( x \) is:
\[ \frac{dt}{dx} = \sec^2 x \quad \Rightarrow \quad dt = \sec^2 x \, dx \]
This means we can replace \( \sec^2 x \, dx \) with \( dt \).
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