1. **State the problem:** Find the integral of the function $5x^2 - 2x$ with respect to $x$. 2. **Recall the formula:** The integral of $x^n$ with respect to $x$ is given by $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. **Apply the integral to each term:** - For $5x^2$, the integral is $$5 \int x^2 \, dx = 5 \cdot \frac{x^{3}}{3} = \frac{5x^3}{3}$$ - For $-2x$, the integral is $$-2 \int x \, dx = -2 \cdot \frac{x^{2}}{2} = -x^2$$ 4. **Combine the results:** $$\int (5x^2 - 2x) \, dx = \frac{5x^3}{3} - x^2 + C$$ 5. **Explain:** We integrated each term separately using the power rule for integration and then combined the results, adding the constant of integration $C$ because indefinite integrals represent a family of functions. **Final answer:** $$\int (5x^2 - 2x) \, dx = \frac{5x^3}{3} - x^2 + C$$