Let $u = \ln x$. Then, $x = e^u$ and $dx = e^u du$. So, we have:
$$\int \sqrt{x} \ln x d x = \int \sqrt{e^u} u e^u du$$
Now, we can simplify the integrand:
$$\int \sqrt{e^u} u e^u du = \int e^{\frac{3}{2}u} u du$$
Now, let's use integration by parts. Recall
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