1. **Problem:** Calculate the indefinite integral $$\int (x + 5)(x - 9) \, dx$$. 2. **Formula and rules:** Use the distributive property to expand the integrand and then integrate term-by-term using the power rule $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$. 3. **Expand the integrand:** $$(x + 5)(x - 9) = x^2 - 9x + 5x - 45 = x^2 - 4x - 45$$ 4. **Integrate each term:** $$\int (x^2 - 4x - 45) \, dx = \int x^2 \, dx - 4 \int x \, dx - 45 \int 1 \, dx$$ 5. **Apply the power rule:** $$\int x^2 \, dx = \frac{x^3}{3}$$ $$\int x \, dx = \frac{x^2}{2}$$ $$\int 1 \, dx = x$$ 6. **Combine results:** $$\frac{x^3}{3} - 4 \cdot \frac{x^2}{2} - 45x + C = \frac{x^3}{3} - 2x^2 - 45x + C$$ **Final answer:** $$\int (x + 5)(x - 9) \, dx = \frac{x^3}{3} - 2x^2 - 45x + C$$