Let $u = \ln x$. Then, $x = e^u$ and $dx = e^u du$. Now we can rewrite the integral in terms of $u$:
$$\int \frac{\ln x}{\sqrt{x}} dx = \int \frac{u}{\sqrt{e^u}} e^u du$$
Now, we can simplify the integral:
$$\int u e^{u/2} du$$
To solve this integral, we can
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