Simple question about direct integration (1 Viewer)

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if I have a equation like this


I know I can integrate so that


but this does not make sense to me because I could think of many U's that if you were to take the derivitive with respect to the squiggly varibale, still includes both variables


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If the derivative with respect to xi includes both variables, then how does it look when you differentiate with respect to both xi and to eta? [Broken]
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