1. The problem is to find the integral $$\int \frac{\ln x}{x} \, dx$$ and match it with one of the given options. 2. Let us use substitution to solve the integral. Set $$u = \ln x$$. 3. Then, the derivative is $$du = \frac{1}{x} dx$$, which means $$dx = x \, du$$. 4. Substitute into the integral: $$\int \frac{\ln x}{x} dx = \int u \, du$$ 5. The integral of $$u$$ with respect to $$u$$ is: $$\int u \, du = \frac{u^2}{2} + C$$ 6. Substitute back $$u = \ln x$$: $$\frac{(\ln x)^2}{2} + C$$ 7. Therefore, the answer is option (d): $$\frac{1}{2} (\ln x)^2$$.