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**TriKri** I guess you mean indefinite multi-dimensional integral. Yes, this was only for the rectangular case, you are right. An arbitrary surface can be varied in an infinite numbers of ways (it can be extended in an infinite number of edge points), hence I believe that it's difficult to find a primitive function from which an integral over an arbitrary surface easily can be expressed, withouth using at least one more integral. And of course it doesn't become easier to find a primitive function which makes any sense when the dimension of the integral increases even more.