To evaluate the integral \( \int (x - 5) \sqrt{x^2 + x} \, dx \), we can follow these steps:
### Step 1: Set up the integral
Let \( I = \int (x - 5) \sqrt{x^2 + x} \, dx \).
### Step 2: Rewrite the integral
We can separate the integral into two parts:
\[
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