1. **State the problem:** We need to evaluate the integral $$\int \frac{x^4 - 3}{x^2} \, dx$$. 2. **Rewrite the integrand:** Simplify the fraction by dividing each term in the numerator by $x^2$: $$\frac{x^4}{x^2} - \frac{3}{x^2} = x^{4-2} - 3x^{-2} = x^2 - 3x^{-2}$$. 3. **Integral formula:** Recall the power rule for integration: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1$$. 4. **Apply the integral:** $$\int (x^2 - 3x^{-2}) \, dx = \int x^2 \, dx - 3 \int x^{-2} \, dx$$ 5. **Integrate each term:** - For $x^2$: $$\int x^2 \, dx = \frac{x^{3}}{3} + C_1$$ - For $x^{-2}$: $$\int x^{-2} \, dx = \frac{x^{-1}}{-1} + C_2 = -x^{-1} + C_2$$ 6. **Combine results:** $$\frac{x^3}{3} - 3(-x^{-1}) + C = \frac{x^3}{3} + 3x^{-1} + C$$ 7. **Final answer:** $$\int \frac{x^4 - 3}{x^2} \, dx = \frac{x^3}{3} + \frac{3}{x} + C$$