1. **State the problem:** Evaluate the integral $$\int e^{\ln x} \, dx$$ and identify the correct answer from the options. 2. **Simplify the integrand:** Recall that $$e^{\ln x} = x$$ for $$x > 0$$ because the exponential and natural logarithm functions are inverses. 3. **Rewrite the integral:** $$\int e^{\ln x} \, dx = \int x \, dx$$ 4. **Integrate:** Using the power rule for integration, $$\int x \, dx = \frac{x^2}{2} + C$$ 5. **Compare with options:** The correct answer is option (c) $$\frac{1}{2} x^2$$. **Final answer:** $$\int e^{\ln x} \, dx = \frac{1}{2} x^2 + C$$