1. The problem is to find the integral of $\ln x$ with respect to $x$. 2. We use integration by parts, which states: $$\int u\,dv = uv - \int v\,du$$ 3. Let $u = \ln x$ and $dv = dx$. Then, $du = \frac{1}{x} dx$ and $v = x$. 4. Applying integration by parts: $$\int \ln x\, dx = x \ln x - \int x \cdot \frac{1}{x} dx = x \ln x - \int 1 dx$$ 5. Simplify the integral: $$x \ln x - x + C$$ 6. Therefore, the integral of $\ln x$ is: $$\int \ln x\, dx = x \ln x - x + C$$ This is the final answer, where $C$ is the constant of integration.