1. **Problem Statement:** Evaluate the integral $$\int \frac{\ln x}{x} \, dx$$. 2. **Formula and Rules:** Recall the integral of the form $$\int \frac{\ln x}{x} \, dx$$ can be approached by substitution or recognizing it as a derivative of a known function. 3. **Step-by-step Solution:** 1. Let $$u = (\ln x)^2$$. Then, $$\frac{du}{dx} = 2 \frac{\ln x}{x}$$. 2. Rearranging, $$\frac{\ln x}{x} = \frac{1}{2} \frac{du}{dx}$$. 3. Therefore, $$\int \frac{\ln x}{x} \, dx = \frac{1}{2} \int du = \frac{1}{2} u + C = \frac{(\ln x)^2}{2} + C$$. 4. **Final Answer:** $$\boxed{\int \frac{\ln x}{x} \, dx = \frac{(\ln x)^2}{2} + C}$$