`intsqrt(2x^2-5x-1)dx`

Explanation

To solve the integral \( \int \sqrt{2x^2 - 5x - 1} \, dx \), we will follow a systematic approach to simplify the expression under the square root and then perform the integration.

### Step-by-Step Solution:

1. **Factor out the coefficient of \(x^2\)**:
\[ \int \sqrt{2x^2 - 5x - 1} \, dx = \int \sqrt{2 \left( x^2 - \frac{5}{2}x - \frac{1}{2} \right)} \, dx \]
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