Integrate : `int xsqrt(x+x^2)dx`

Explanation

To solve the integral \( \int x \sqrt{x + x^2} \, dx \), we can follow these steps:

### Step 1: Simplify the integrand
We start by rewriting the expression under the square root:
\[ \sqrt{x + x^2} = \sqrt{x(1 + x)} = \sqrt{x} \sqrt{1 + x} \]
Thus, the integral becomes:
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