1. Problem: Calculate the integral $$\int x^2 (8x^3 - 6) \, dx$$ 2. Use the distributive property to expand the integrand: $$x^2 (8x^3 - 6) = 8x^{5} - 6x^{2}$$ 3. Now integrate term by term using the power rule $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$: $$\int (8x^{5} - 6x^{2}) \, dx = 8 \int x^{5} \, dx - 6 \int x^{2} \, dx$$ 4. Calculate each integral: $$8 \times \frac{x^{6}}{6} - 6 \times \frac{x^{3}}{3} = \frac{8}{6} x^{6} - 2 x^{3}$$ 5. Simplify the coefficients: $$\frac{4}{3} x^{6} - 2 x^{3} + C$$ Final answer: $$\int x^2 (8x^3 - 6) \, dx = \frac{4}{3} x^{6} - 2 x^{3} + C$$