1. The problem is to find the indefinite integral of the function $x^2 - 6x + 2$ with respect to $x$. 2. The formula for integrating a polynomial term $x^n$ is $$\int x^n dx = \frac{x^{n+1}}{n+1} + C,$$ where $C$ is the constant of integration. 3. Apply the integral to each term separately: $$\int (x^2 - 6x + 2) dx = \int x^2 dx - 6 \int x dx + 2 \int dx.$$ 4. Calculate each integral: - $$\int x^2 dx = \frac{x^{3}}{3}$$ - $$\int x dx = \frac{x^{2}}{2}$$ - $$\int dx = x$$ 5. Substitute back: $$\frac{x^{3}}{3} - 6 \cdot \frac{x^{2}}{2} + 2x + C = \frac{x^{3}}{3} - 3x^{2} + 2x + C.$$ 6. Therefore, the integral of $x^2 - 6x + 2$ with respect to $x$ is: $$\boxed{\frac{x^{3}}{3} - 3x^{2} + 2x + C}.$$