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When solving an integral (if possible), the solution generally entails applying a substitution, transformation, or "trick" that reduces/simplifies the original integral into known results. When should an integral be considered a duplicate, if after one or more transformations, the rest of the calculations are available on another post?

The question arose from this post. After a single substitution (provided in the comments), the transformed integral is identical to the one asked in the duplicate post. In this case, I can see why my original question is considered a duplicate (only requiring one step to become identical). Another example of this (I am sure there are many more as well) is this post, where the original integral was solved by differentiating and using another result. I think these two examples are essentially the same: they both require one step/trick to become identical to a previously answered result (should the second example also be considered a duplicate?).

However, at what point can we consider one integral a duplicate of another? How many "steps" determine whether if an integral question is a duplicate of another, or is the decision relatively subjective? This meta post is related, asking "If the answer to question B answers question A, should question A be considered a duplicate?" There seem to be a lot of posts concerned with dealing with duplicates; however, I am interested how the decision is made with integration questions.

Thanks.

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    $\begingroup$ Relatively subjective, Maxime. I couldn't imagine it any other way. We should have a list of sufficient conditions (close as duplicate if ... is true) and necessary conditions (if this is closed as a duplicate then ... should be true) for these things, but beyond that any amount of legislation would be too context-specific and better left to voting systems. For example, if the question is literally the same, that's a sufficient condition. But a necessary condition would be that the OP of dupe should be able to understand how the two integrals are related. $\endgroup$ Commented Jan 22 at 5:13
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    $\begingroup$ More broadly, there are many cases of "abstract duplicates" where identical reasoning applies, though the context is different. Sometimes the translation between the two is entirely clear, other times a sentence or two might be helpful/needed. Very subjective. $\endgroup$ Commented Jan 22 at 13:45

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This is not restricted to integrals. If question B is equivalent to question A via a very simple argument (for example, a straight forward substitution in case of integrals), then question B should be closed as a duplicate of question A, and one of the close voters should explain this simple argument in the comments.

The problem here is that "simple" is very subjective. What is simple and takes like 5 seconds of thought for an experienced mathematician can take a week for a less experienced student. So be careful. Some users are taking this too far and close everything as a duplicate even if the argument that it's a duplicate requires a considerable effort (for the OP) and many steps (1, 2, 3). This is not OK in my opinion.

To prevent that a question gets closed without the OP getting the answer they need, you can do the following:

  • Explain in a comment that question B is a duplicate of A because of [simple argument].
  • Wait for feedback by the OP if they understand [simple argument].
  • If yes, cast a close vote.
  • If not, elaborate the [simple argument] in an answer. (Please do not explain the simple argument further in the comments, do that in an answer.)
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As maybe somewhat unsatisfying answer, I would say it doesn't matter that much where you draw the line. IMHO, liberally marking something as duplicate is probably fine as long as an explanation is provided how you get your answer from the linked question or its answers.

I don't have an integral related example but as a somewhat similar example I asked about the eigenvalues and eigenvectors of a certain matrix. It was then marked as a duplicate to a question where the asker considers what is essentially its inverse matrix (up to a permutation that reverses the order of the indices). Could one have expected me to find that question on my own? I don't think so since the connection wasn't at all obvious on the surface. Do I mind that my question was marked as duplicate? Not at all. After all, I got the answer I wanted and anyone reading my question can get it too.

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