How does integration by parts work with multivariable function? Lets say I have the functions $f(\textbf{x})$ and $g(\textbf{x})$, where $\textbf{x}\in\mathbb{R}^n$. How would integration by parts be implemented in this case? Example? I came a cross into this subject because in my study material I have an multidimensional integral and I'm supposed to use integration by parts in it. I searched Wikipedia for answer but the explanation is kinda short so I was hoping for better detailed explanation from here :)
Here is my reference where I came up with my question:
