The formula for integration by parts is:
$$\int u \, dv = uv - \int v \, du$$
In this case, we can choose $u = \ln x$ and $dv = x^3 \, dx$. This means that $du = \frac{1}{x} \, dx$ and $v = \frac{1}{4}x^4$.
Using the formula, we have:
$$\int x^3 \ln x \, dx =
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