Integrate the functions`x/(sqrt(x+4)), x >0`

Explanation

To solve the integral \( I = \int \frac{x}{\sqrt{x+4}} \, dx \), we can follow these steps:

### Step 1: Substitute \( x + 4 = t^2 \)
Let \( x + 4 = t^2 \). Then, we differentiate both sides to find \( dx \):
\[ dx = 2t \, dt \]
From the substitution, we can express \( x \) in terms of \( t \):
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