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How can you prove that a function has no closed form integral?

When they say that, e.g., Li(x) has no closed form (for some agreed upon definition of "closed form"), do they mean that it can be proved that there isn't one, or just that none has been found yet. Most authors seem to just assert that a given integral can't be represented in any simpler way, but I've been wondering if that's because they know this for a fact, or just that it's assumed that if there is one it would have been found by now.

If this is a theorem, how would you go about proving it?


marked as duplicate by Jonas Meyer, Arturo Magidin, Ross Millikan, Aryabhata, J. M. is a poor mathematician Dec 31 '10 at 2:09

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    $\begingroup$ Joshua Frank, I'm sorry we had to close your first question on the site, but it looks like answers to the linked question should answer your question. I hope you stick around, and if you have questions not resolved at the link, please feel free to ask them. $\endgroup$ – Jonas Meyer Dec 31 '10 at 2:23
  • $\begingroup$ I guess that is a duplicate, but it's weird because I did search for an existing answer before posting and didn't come across the linked answer. Not sure why it wasn't found. Thanks for the link. $\endgroup$ – Joshua Frank Jan 1 '11 at 4:00