I'm not sure how to phrase this question. I'm sure I could write it in terms of operators between Frechet spaces, or something like that. Let me apologies to any analysts in advance for my lack of rigor.
I'm basically interested in "how many" elementary functions have elementary anti-derivatives. I realize that I ought to impose some conditions on the functions, e.g. differentiable, and on the domains of definition.
It would be great if someone could give an answer which puts this question in to the correct language, provide sufficient restrictions and then state any known results. Sorry to be so wishy-washy!
