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I want to know whether "partial integration" exists analogous to partial differentiation in ordinary calculus for functions of several variables.

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    partial integration is synonym for [integration by parts](http://en.wikipedia.org/wiki/Integration_by_parts)2011-11-07
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    If I understand the question correctly, I'd say yes. For example, you can compute $\int x^2+3y^2 \, dy= yx^2+y^3 +C(x)$ (the constant of integration becomes an arbitrary function of $x$).2011-11-07
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    I think you're looking for [line integrals](http://en.wikipedia.org/wiki/Line_integral), possibly along a coordinate line.2011-11-07
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    @pedja No, partial derivatives are looking at the change in only one coordinate. Integration by parts is undoing the product rule.2011-11-07
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    @Graphth [partial integration](http://en.wikipedia.org/wiki/Partial_integration)2011-11-07
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    @pedja I see, but the point of the question is to find an integration that is analogous to partial derivatives. Is integration by parts analagous to partial derivatives? I don't think so. So, it's just that the OP doesn't know the correct term. Your comment is saying that term already exists but doesn't describe what the OP is asking about?2011-11-07
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    @Graphth,I just pointed out on wrong use of the term2011-11-07
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    @pedja Okay, sorry, I misunderstood.2011-11-07
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    @pedja To the best of my knowledge, "partial integration" used to refer to integration by parts is just a mistranslation of the German term and as a calque for other foreign terms. In my American courses "partial integration" and "integration by parts" have always been distinct concepts, the former actually being an inverse operation to partial differentiation.2016-11-05

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