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> I don't think it makes sense to the same degree. Simple compositions of elementary functions, e.g. exp(x^2), do not have indefinite integrals. While it's cle
by JadeNB 6y ago
> I don't think it makes sense to the same degree. Simple compositions of elementary functions, e.g. exp(x^2), do not have indefinite integrals.
While it's clear what you meant, it's mathematically important to note that functions like yours, and, indeed, all continuous functions, definitely do have indefinite integrals—that of `exp(x^2)` even has a name (https://mathworld.wolfram.com/Erfi.html); https://mathworld.wolfram.com/Erfi.html); those integrals just aren't elementary, in the same technical sense in which you are using the word (https://en.wikipedia.org/wiki/Elementary_function https://en.wikipedia.org/wiki/Elementary_function).
- ohsonice 6y agoYour first link is not working for me on mobile. Thanks for the clarification though. Exp(x^2) is a finite composition of a polynomial and an exponential function so from what you posted, it does fall into the Wikipedia definition of elementary function.
- brewmarche 6y agoThe first link of your parent should've been https://mathworld.wolfram.com/Erfi.html https://mathworld.wolfram.com/Erfi.html They were arguing that the antiderivative F of f: x ↦ exp(x²) is not elementary, whereas f itself is elementary. But both F and f are well-defined functions, which means that f has an indefinite integral, it just happens to be not elementary.
- JadeNB 6y ago> The first link of your parent should've been https://mathworld.wolfram.com/Erfi.html https://mathworld.wolfram.com/Erfi.html Sometimes Markdown eats following parentheses and sometimes it doesn't, and I've never figured out why. When I first viewed the post it showed me the parenthesis not being eaten, but then it did it anyway when I viewed it from the main page (too late for me to edit). Thanks for fixing it up!