Let's choose $u = \ln x$ and $dv = x dx$.
Differentiating $u$ with respect to $x$, we get $du = \frac{1}{x} dx$.
Integrating $dv$ with respect to $x$, we get $v = \frac{1}{2}x^2$.
Now, we can use the formula for integration by parts:
$$\int u dv = uv -
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