# Iterated integration by parts with multiple variables

Let $$\alpha$$ be multi-index. Consider the iterated integral $$\int_{a_n}^{b_n} \cdots \int_{a_1}^{b_1} \left(D^{\alpha}f(x)\right)g(x) \, \mathrm{d}x_1 \ldots \mathrm{d}x_n.$$ Does anyone know a slick formula for this, moving all derivatives from $$f$$ to $$g$$? Of course, this is just iterated integration by parts, but doing this by hand seems like a huge pain. A simple reference would be sufficient, thanks!