1. **State the problem:** Find the integral $$\int 10x^4 \, dx$$. 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 and $$n \neq -1$$. 3. **Apply the formula:** Here, $$n=4$$, so $$\int 10x^4 \, dx = 10 \int x^4 \, dx = 10 \cdot \frac{x^{4+1}}{4+1} + C = 10 \cdot \frac{x^5}{5} + C$$ 4. **Simplify:** $$10 \cdot \frac{x^5}{5} + C = \cancel{10} \cdot \frac{x^5}{\cancel{5}} + C = 2x^5 + C$$ 5. **Final answer:** $$\boxed{2x^5 + C}$$