1. **State the problem:** Evaluate the integral $$\int (4x^3 - 7x + 2) \, dx$$. 2. **Recall the formula:** The integral of a polynomial term $$ax^n$$ is given by $$\int ax^n \, dx = \frac{a}{n+1} x^{n+1} + C$$, where $$C$$ is the constant of integration. 3. **Apply the formula to each term:** - For $$4x^3$$: $$\int 4x^3 \, dx = 4 \cdot \frac{x^{3+1}}{4} = x^4$$ - For $$-7x$$: $$\int -7x \, dx = -7 \cdot \frac{x^{1+1}}{2} = -\frac{7}{2} x^2$$ - For $$2$$: $$\int 2 \, dx = 2x$$ 4. **Combine all results:** $$\int (4x^3 - 7x + 2) \, dx = x^4 - \frac{7}{2} x^2 + 2x + C$$ 5. **Final answer:** $$x^4 - \frac{7}{2} x^2 + 2x + C$$