1. **Problem:** Find the indefinite integral $\int 6x^4 \, dx$. 2. **Formula:** The power rule for integration states: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad n \neq -1$$ 3. **Apply the formula:** Here, $n=4$, so $$\int 6x^4 \, dx = 6 \int x^4 \, dx = 6 \cdot \frac{x^{4+1}}{4+1} + C = 6 \cdot \frac{x^5}{5} + C$$ 4. **Simplify:** $$= \frac{6}{5} x^5 + C$$ 5. **Answer:** $$\int 6x^4 \, dx = \frac{6}{5} x^5 + C$$ This completes the first problem step-by-step.