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

Explanation

To solve the integral \(\int \frac{x+2}{\sqrt{4x - x^2}} \, dx\), we will follow a systematic approach.

### Step 1: Rewrite the Integral
We can express the integral in a more manageable form. We will separate the numerator \(x + 2\) into a form that can be differentiated.

\[ \int \frac{x+2}{\sqrt{4x - x^2}} \, dx = \int \frac{-\frac{1}{2}(4 - 2x) + 4}{\sqrt{4x - x^2}} \, dx \]
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