1. **State the problem:** We need to evaluate the integral $$\int \frac{x^3 + 5x^2 - 4}{x^2} \, dx$$. 2. **Rewrite the integrand:** Divide each term in the numerator by $x^2$: $$\frac{x^3}{x^2} + \frac{5x^2}{x^2} - \frac{4}{x^2} = x + 5 - 4x^{-2}$$ 3. **Express the integral with simplified terms:** $$\int (x + 5 - 4x^{-2}) \, dx$$ 4. **Integrate each term separately:** - Integral of $x$ is $$\frac{x^2}{2}$$ - Integral of $5$ is $$5x$$ - Integral of $-4x^{-2}$ is $$-4 \int x^{-2} \, dx = -4 \left(-x^{-1}\right) = 4x^{-1}$$ 5. **Combine the results:** $$\frac{x^2}{2} + 5x + 4x^{-1} + C$$ 6. **Final answer:** $$\boxed{\frac{x^2}{2} + 5x + \frac{4}{x} + C}$$