1. **State the problem:** Calculate the integral $$\int \frac{1 + x + x^2}{x^4} \, dx$$. 2. **Rewrite the integrand:** Divide each term in the numerator by $x^4$: $$\frac{1}{x^4} + \frac{x}{x^4} + \frac{x^2}{x^4} = x^{-4} + x^{-3} + x^{-2}$$. 3. **Integral formula:** Recall that $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ for $n \neq -1$. 4. **Integrate term-by-term:** $$\int x^{-4} \, dx = \frac{x^{-3}}{-3} = -\frac{1}{3x^3}$$ $$\int x^{-3} \, dx = \frac{x^{-2}}{-2} = -\frac{1}{2x^2}$$ $$\int x^{-2} \, dx = \frac{x^{-1}}{-1} = -\frac{1}{x}$$ 5. **Combine results:** $$\int \frac{1 + x + x^2}{x^4} \, dx = -\frac{1}{3x^3} - \frac{1}{2x^2} - \frac{1}{x} + C$$ **Final answer:** $$\boxed{-\frac{1}{3x^3} - \frac{1}{2x^2} - \frac{1}{x} + C}$$