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When does a function NOT have an antiderivative?

This question was closed as a duplicate. I agree that the question was a duplicate (although I would have also added a second link, one to some post that discusses whether $(a^b)^c\overset?=(a)^{b^c}$, because this seems to be the main source of confusion here).

But anyway, let us assume that the question is rightfully closed as a duplicate. My main concerned is that it was also deleted, which strikes me as inappropriate. Can someone please explain to me why this question was deleted?

I read some posts here on meta, and there seems to be some consensus that well received, duplicate questions are indeed useful, and so they need not be deleted. Being a duplicate is not, by itself, a reason for deletion. So it seems that, in this particular case, there was something else that triggered the deletion. Can someone please explain what happened? Thanks!

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    $\begingroup$ Duplicates must meet a higher standard. They must justify their existence. They should have good unique answers, or be dissimilarly worded to aid searchability. They also need to be good questions. This question in particular vaguely straddles two questions: "Why is $e^{2x} \neq e^{x^2}$?" and "How do we show a function has no elementary anti-derivative?". The asker got their answer (which is good), but now the site really has no more need for this question. $\endgroup$ – Theo Bendit Apr 28 at 2:16
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    $\begingroup$ @TheoBendit: Your view differs from mine. In particular I'd never looked at $e^{2x} \neq e^{x^2}$ in connection with the issue of no elementary anti-derivative for the latter. That strikes me as a dissimilar wording "to aid searchability" worth keeping around. In fact my standards for deleting content are for stuff that is so bad it cannot be made useful without radical changes. $\endgroup$ – hardmath Apr 28 at 4:19
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I've had calc students make the $e^{x^2}=e^{2x}$ mistake before, as non-associativity of exponentiation does not come up very often in lower level coursework. Beings that $\int e^{x^2}$ is often brought up specifically as a first example of an integral with no closed form, I would expect many users who find this question through search to naturally follow the path to the duplicate target, whether or not they were looking for that originally. There is clear future value here.

It should not have been deleted. Please keep in mind that duplicate questions should not be deleted unless the question is very low quality, the wording is very similar to its duplicate target, or the duplicate target is closed for other (quality related) reasons.

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  • $\begingroup$ If the target is closed for other reasons, how is that a reason to delete the duplicate? $\endgroup$ – Henning Makholm Apr 30 at 15:40
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    $\begingroup$ @HenningMakholm The idea would be that if the target is closed for quality related reasons (by this I mean, roughly, "being an inherently bad question") then purportedly the duplicate would be as well, and both would be on their way to deletion. On a related note, if, for example, you had a question closed as unclear and the same question was asked again later but with perfect clarity, you wouldn't want to close (much less delete) the latter as a duplicate of the former. $\endgroup$ – Alexander Gruber Apr 30 at 19:38

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