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This is a very known result, but I don't have some proof. Someone known or has some proof of it?

Let be $\omega = P\;dx + Q\;dy$ be a $C^1$ differential form on a domain $D$. If $$\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x} ,$$ then $\omega$ is locally exact.

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    This is the [Poincaré-lemma in its most basic form](http://en.wikipedia.org/wiki/Poincare_lemma#Poincar.C3.A9_lemma). Since this is closely related to your [other question](http://math.stackexchange.com/questions/87577/closed-forms-and-a-simple-relation-with-cauchy-riemann) I strongly recommend that you do some reading on [differential forms](http://en.wikipedia.org/wiki/Differential_form) and the wedge product (written $\wedge$)2011-12-02
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    Cartan's book *Elementary theory of analytic functions ...* gives [a very readable answer](http://books.google.com/books?id=KsGbqTBjyoUC&pg=PA49) to your question.2011-12-02

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