Integrate the functions`sqrt(x^2+3x)`

Explanation

To integrate the function \( \sqrt{x^2 + 3x} \), we will follow a systematic approach to simplify the integrand and then apply integration techniques.

### Step-by-Step Solution:

1. **Complete the Square:**
We start by rewriting the expression inside the square root:
\[
x^2 + 3x = (x^2 + 3x + \frac{9}{4}) - \frac{9}{4} = \left(x + \frac{3}{2}\right)^2 - \frac{9}{4}
...