1. **State the problem:** We need to find the indefinite integral of the function $$16x^7 - 7x^6 - 18x^5$$ 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 formula to each term:** $$\int (16x^7 - 7x^6 - 18x^5) dx = \int 16x^7 dx - \int 7x^6 dx - \int 18x^5 dx$$ 4. **Integrate each term:** $$\int 16x^7 dx = 16 \cdot \frac{x^{7+1}}{7+1} = 16 \cdot \frac{x^8}{8}$$ $$\int 7x^6 dx = 7 \cdot \frac{x^{6+1}}{6+1} = 7 \cdot \frac{x^7}{7}$$ $$\int 18x^5 dx = 18 \cdot \frac{x^{5+1}}{5+1} = 18 \cdot \frac{x^6}{6}$$ 5. **Simplify each term:** $$16 \cdot \frac{x^8}{8} = \cancel{16} \cdot \frac{x^8}{\cancel{8}} = 2x^8$$ $$7 \cdot \frac{x^7}{7} = \cancel{7} \cdot \frac{x^7}{\cancel{7}} = x^7$$ $$18 \cdot \frac{x^6}{6} = \cancel{18} \cdot \frac{x^6}{\cancel{6}} = 3x^6$$ 6. **Combine the results and add the constant of integration:** $$\int (16x^7 - 7x^6 - 18x^5) dx = 2x^8 - x^7 - 3x^6 + C$$ **Final answer:** $$\boxed{2x^8 - x^7 - 3x^6 + C}$$