1. **Problem:** Evaluate the integral $$\int x^3 \, dx$$. 2. **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 $$n \neq -1$$ and $$C$$ is the constant of integration. 3. **Apply the formula:** Here, $$n = 3$$, so: $$\int x^3 \, dx = \frac{x^{3+1}}{3+1} + C = \frac{x^4}{4} + C$$. 4. **Explanation:** We increase the power by 1 and divide by the new power. 5. **Final answer:** $$\frac{1}{4} x^4 + C$$.