1. **State the problem:** Evaluate the indefinite integral $$\int 8 \sin^2(x) \cos(x) \, dx$$. 2. **Recall the formula and substitution method:** When an integral involves a function and its derivative, substitution is useful. Here, notice that the derivative of $\sin(x)$ is $\cos(x)$, which appears in the integral. 3. **Set the substitution:** Let $$u = \sin(x)$$, then $$du = \cos(x) \, dx$$. 4. **Rewrite the integral in terms of $u$:** $$\int 8 \sin^2(x) \cos(x) \, dx = \int 8 u^2 \, du$$. 5. **Integrate with respect to $u$:** $$\int 8 u^2 \, du = 8 \int u^2 \, du = 8 \cdot \frac{u^3}{3} = \frac{8}{3} u^3$$. 6. **Substitute back $u = \sin(x)$:** $$\frac{8}{3} \sin^3(x) + C$$. **Final answer:** $$\int 8 \sin^2(x) \cos(x) \, dx = \frac{8}{3} \sin^3(x) + C$$.