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This MathSE posted question is excerpted below:

$$\int \frac{x+3}{x^2+5x+2}$$

besides going with imaginary numbers how should I proceed to solve this integral?

I was trying to factorize the denominator to use partial fractions but failed.

If there are no other methods faster than the imaginary solution I would like to see the imaginary solution

I then responded with the following comment:

$$\int \frac{x+3}{x^2+5x+2} = \int \frac{(1/2)(2x+5)}{x^2+5x+2} + \frac{1/2}{(x + 2.5)^2 - \left[\sqrt{4.25}\right]^2} $$

Subsequently, one of the moderators deleted my comment, and then later explained their actions by

Yes, because it is against site policy to answer questions in the comments.

Is my comment an answer, or is it a (very incomplete) guide as to how the OP (i.e. original poster) should plan their attack of the problem? Is it plausible that my comment will provide a link to the OP's tools (i.e. previously solved problems, worked examples, theorems)?

For what it's worth, the OP subsequently asked in a comment (which has now been deleted) how I factored the denominator in the second fraction. Can one infer from the OP's subsequent question that the OP does not consider the originally posted question answered by the comment?

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    $\begingroup$ I am of the opinion that such a comment does not constitute as an answer as much as it does a simple hint. I don’t believe it is worth a deletion let alone the size of an average answer post to be recognised as such. $\endgroup$
    – KStar
    Commented Dec 2, 2023 at 21:10
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    $\begingroup$ Playing devil's advocate a tad: if the question is low-quality, why even offer a hint? $\endgroup$
    – PrincessEev
    Commented Dec 2, 2023 at 22:17
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    $\begingroup$ @PrincessEev Usually I don't offer a hint. In this case, while the question was of low quality with respect to MathSE protocol, the posted question clearly indicated some attempt to solve the problem. Further, I surmised that the OP might well have been given an assortment of tools, and simply chose the wrong tool to explore. My comment hint was intended to guide the OP towards the tool that I suspected that the problem composer had intended. $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 22:20
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    $\begingroup$ I'm not sure how to balance your judgement that "the question was of low quality with respect to MathSE protocol" with the importance you seem to attach to your original comment and to the OP's request for clarification "how I factored the denominator in the second fraction." MathSE does not require that Questions are posed at a certain level (here perhaps a high school or freshman calculus course), and we don't demand that such Questions be posed perfectly. Indeed pointing out errors in the problem statement can be included in an Answer that solves under a reasonable interpretation. $\endgroup$
    – hardmath
    Commented Dec 3, 2023 at 1:48
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    $\begingroup$ @hardmath At the time of my comment, the posted question was nothing more than a PSQ, and a vague reference to imaginary numbers, as excerpted in the posted math-meta question. To me, this implies that I am not allowed to answer the question. The deletion of my comment was originally justified by indicating that you can't provide answers in the comments. It seemed obvious to me that the OP had simply looked at the wrong tool, so my comment showed him the right tool, but still left him significant thinking+work to do. ...see next comment $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 2:15
  • $\begingroup$ @hardmath The point of the last paragraph in my posting was merely to provide further evidence that it is ridiculous to characterize my comment as an answer; you simply have to consider whether the OP thinks the question was answered. Notice that my initial comment to the posting was a reference to a protocol article, as a reaction to the PSQ. Subsequently, one of the answers, which now has a score of +7, avoids the issue of whether my comment answered the question, by referring to a Help Center article. ...see next comment $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 2:19
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    $\begingroup$ @hardmath As I commented following the Help-Center answer, I consider that justification bizarre. It is very obvious that hint-comments are very widespread and (I strongly suspect) a better indicator of the will of the majority than reactions to this math-meta posting. For what it's worth, I understand the fear of a slippery slope. That is, other comments do occasionally abuse the rule by providing a complete answer. However, this action against my specific comment seems extreme. $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 2:24
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    $\begingroup$ Your comment isn't an answer to the question and I wouldn't have deleted it. I must say though, that when OP responded asking "how I[you] factored the denominator in the second fraction", I mean, it's completion of the square, which is a formula taught well before integration. Your comment would have been an "answer" if you were dealing with a poster who could actually follow it. This OP looked like the only thing they knew was standard formulas and they desperately tried to fit what you wrote into that format, so the comment didn't really work though that is completely OP's fault. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Dec 4, 2023 at 7:08
  • $\begingroup$ @SarveshRavichandranIyer What do you think of the moderator's subsequently justifying their action with the Help Center article? $\endgroup$
    – user2661923
    Commented Dec 4, 2023 at 8:22
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    $\begingroup$ @user2661923 That article is applicable when the comment is something that would be an answer if copy-pasted into an answer box. You'd strive to make your answer more complete than your comment. So, your comment isn't an answer, or even an attempt at it. I wouldn't even call it a hint but that's only after seeing the OP's response, who was clueless even after it. The moderator thought otherwise, and I'm not with them on this occasion. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Dec 4, 2023 at 8:28
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    $\begingroup$ YES your comment should have been deleted. And I realize the irony here, As I am now the one answering a question in the comments! $\endgroup$
    – Mike
    Commented Dec 4, 2023 at 18:17
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    $\begingroup$ Well, I myself really don't care about the majority view on this. I admit it. And whether your view is the majority, is not at all clear to me. There may be a loud minority who agree with you and who are leaving all the comment-answers. $\endgroup$
    – Mike
    Commented Dec 4, 2023 at 18:39
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    $\begingroup$ Yes I do think moderators should delete hint-comments whenever they find them...no matter how widespread the custom is. $\endgroup$
    – Mike
    Commented Dec 4, 2023 at 18:42
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    $\begingroup$ I'm not sure what you mean there though. If you really feel MSE should get official recognition as a sort of online-office-hours/homework-helpers site, and you are using as reasoning for this that your view represents the majority, then at the very least, you should find a majority who agrees with you. A certain number of prolific comment-answerers is not a majority. Your OP is now at +1 upvote here whereas the two answers disagreeing with you are at +7 and +10 upvotes, at the time of this writing. $\endgroup$
    – Mike
    Commented Dec 4, 2023 at 18:53
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    $\begingroup$ @Mike Wrong strategy; not a good idea to attempt to combat a subjective issue that facilitates one or both sides emotionally digging their heels in. See the Psychological warfare comment that I left, in response to the comment of D.W., following the answer of Xander Henderson. It is far better to wait for the moderator to upset many, many, others, and then refer the others to this meta-math article. $\endgroup$
    – user2661923
    Commented Dec 4, 2023 at 19:05

2 Answers 2

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Per the Math SE Help Center:

What are comments?

Comments are temporary "Post-It" notes left on a question or answer. They can be upvoted (but not downvoted) and flagged, but do not generate reputation. There's no revision history, and when they are deleted they're gone for good.

...

When should I comment?

You should submit a comment if you want to:

  • Request clarification from the author;
  • Leave constructive criticism that guides the author in improving the post;
  • Add relevant but minor or transient information to a post (e.g. a link to a related question, or an alert to the author that the question has been updated).

When shouldn't I comment?

Comments are not recommended for any of the following:

...

  • Answering a question or providing an alternate solution to an existing answer; instead, post an actual answer (or edit to expand an existing one);

  • Secondary discussion or debating a controversial point; please use chat instead;

  • Discussion of community behavior or site policies; please use meta instead.

Note that the Help Center emphasizes that comments are temporary and transient. They are not supposed to be a permanent part of the record of the site. The Help Center specifically admonishes users not to post answers in the comments. Hints are in a little more of a grey area, but since hints neither suggest changes to a post nor explicitly ask for clarification, they fall under the category of "secondary discussion".

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    $\begingroup$ Do you actually intend to delete every hint-comment on every mathSE post? Comment-hints to get the OP thinking are extremely common place. If this Help-Article represents the will of the majority, then why are Comment-hints so frequently given? $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 21:32
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    $\begingroup$ @user2661923 Please do not engage in whataboutism. I delete comments that do not follow the rules when (1) I come across them organically (as I did in this case), or (2) they are flagged for deletion by other users. The fact that a small number of moderators cannot possibly delete every comment which doesn't follow the rules does not mean that we shouldn't enforce the rules when we see them being broken. This is similar to the way in which speed limits are enforced on the highways: you can't catch every speeder, but you do your best. $\endgroup$
    – Xander Henderson Mod
    Commented Dec 2, 2023 at 21:34
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    $\begingroup$ Your missing the point of my comment. I allege that the Help-Article does not even come close to representing the will of the majority. Normally, such minority views are harmless when they are ignored. However, when you start to enforce such a minority view, then the issue needs to be raised. $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 21:40
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    $\begingroup$ @user2661923 The hints can be useful, to write a proper answer with. Once the answer has arrived, the comment is obsolete. If no answer arrives, the comment is also obsolete. Apparently it wasn't good enough to make an answer on. $\endgroup$
    – Mast
    Commented Dec 2, 2023 at 21:40
  • $\begingroup$ @Mast The hint-comment was deleted before the comment was closed, but after the moderator referred the OP to other MathSE articles, many of which gave more complicated Math, and one of which had an answer that followed a strategy similar to my comment-hint. $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 21:42
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    $\begingroup$ Comments are intended to clarify or improve the question/answer and are ephemeral. Comments also can't be downvoted, nor edited by others. A partial answer that can be improved by later edits is preferable to a comment that is frozen. Look to Puzzling.SE to see how they handle half-answers. $\endgroup$
    – Criggie
    Commented Dec 2, 2023 at 21:49
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    $\begingroup$ @Criggie Generally, a hint-comment is an opportunity to influence the OP to think about how to solve the problem. When coupled with a reference to one of the meta.math protocol articles, it provides a guide to the OP about how to improve this specific question. I consider this better than making abstract references to (for example) context, showing work, or tools. At least this way, the OP has been given some realistic chance at no longer being overwhelmed by the question, without MathSE protocol being violated. $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 21:54
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    $\begingroup$ For what's it's worth, I regard it as an open issue whether the majority feel that MathSE's priority should be a high quality repository versus an educational vehicle. Setting that issue aside, continuing to give priority to the quality of the repository, the use of comment-hints seems a reasonable compromise towards those reviewers (who might be in the majority) that the primary focus should be education. $\endgroup$
    – user2661923
    Commented Dec 2, 2023 at 22:32
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    $\begingroup$ @user2661923, If you want to argue for a particular policy on comments, I don't think debating it in the comments here is the most effective way. I would suggest spending some time to educate yourself about the arguments pro and con (there has been a lot already written on this subject), then come up with a specific proposal, and make a separate post on meta with your policy proposal and request feedback. I think that gives you a better chance of influencing future site policy than a discussion/debate in the comments under Xander's answer explaining the site's current policy. $\endgroup$
    – D.W.
    Commented Dec 3, 2023 at 0:01
  • $\begingroup$ @D.W. Psychological warfare is where you find it. Better to wait to see if the behavior against hint-comments that are clearly not answers continues, which will then only be justified by the (bizarre) Help-Center article. Then, as more and more reviewers see their hint-comments deleted, I can surgically reference this entire math-meta article for their review, shortly after the comment deletion. Fighting city-hall is tricky. $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 2:34
  • $\begingroup$ @Jean-ClaudeArbaut Appreciate your injecting a note of rational thought into the discussion. There is a prevailing issue which seems to have been generally ducked: Was my comment an answer? The comment certainly has the potential to be developed into an answer. ...see next comment $\endgroup$
    – user2661923
    Commented Dec 8, 2023 at 17:56
  • $\begingroup$ @Jean-ClaudeArbaut However, given that the issue of integrating $~\displaystyle \int \frac{dx}{(ax + b)^2 - c^2} ~$ was not addressed, and given the OP's reaction of "those are different questions" to previous attempts to help them, I don't see how my comment could be reasonably regarded as an answer. This view was subsequently supported by the OP's subsequent questioning about how I (in effect) completed the square in the denominator. I was forced into meta-math because there was no other recourse, given the moderator's actions. ...see next comment $\endgroup$
    – user2661923
    Commented Dec 8, 2023 at 17:59
  • $\begingroup$ @Jean-ClaudeArbaut Normally, I prefer to stay away from meta-math because of the tendency of MathSE reviewers to dig their heels in. To me, the issues in this article are simple and have been generally ignored: Was the comment an answer? Should comments that lay the groundwork for an answer but are not an answer themselves be deleted? To what extent does common practice versus math.meta article voting provide an indicator of the will of the majority? How important is the will of the majority? $\endgroup$
    – user2661923
    Commented Dec 8, 2023 at 18:03
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    $\begingroup$ I will also point out, @user2661923, that you seem to want to make an appeal to the majority. Policies on Meta are decided by voting. Right now, 12 people have agreed with the answer that I have provided. 6 people have agreed with D.W.'s answer, and two have disagreed (though it is unclear which parts they have disagreed with). 8 people have agreed with your question, while another 8 have disagreed (I don't really know how to interpret that). The only metrics we have seem to indicate that you are not a representative of the majority. $\endgroup$
    – Xander Henderson Mod
    Commented Dec 8, 2023 at 18:40
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    $\begingroup$ @user2661923 How do you explain the large number of people who drive 90 miles per hour on the interstate? $\endgroup$
    – Xander Henderson Mod
    Commented Dec 8, 2023 at 18:42
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Yes. Absolutely. Deleting your comment was appropriate, based on how Stack Exchange works. Under Stack Exchange norms, that didn't belong in a comment. I recommend that you avoid answering questions in the comments. If you want to answer the question, post it in the 'Your Answer' box.

The question asked "how should I proceed to solve this integral?" and your comment described an approach to proceed to solve the integral. In other words, your comment contained an answer to the question that was asked. That's not what comments are intended for.

Comments are not intended for complete answers; for an answer that seems "too short" to "deserve" being a full answer; for partial answers (I would suggest); for hints in lieu of an answer (I would suggest). Comments are intended to help improve the question, or to alert readers to related questions, or for other transient purposes, and are liable to be deleted at any time.

References: How do comments work?, https://rpg.meta.stackexchange.com/q/6533/10751, https://interpersonal.meta.stackexchange.com/q/1644/1710,

Separately: I encourage folks to consider refraining from answering questions that you consider low-quality, or even giving partial solutions to such questions. Answering such questions encourages and incentivizes people to continue posting low-quality questions. So it might be better for the community and health of the site if people declined to answer, or partially answer, such questions, until the question has been improved to meet site standards, and instead left comments educating the poster about site standards. I realize the positive motivation to try to help the individual who posted the question, and I find that laudable. At the same time I hope folks will balance that against the potential harm to the site of rewarding this kind of behavior. As always, it is up to you and your individual conscience. Thank you for considering it.

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    $\begingroup$ Shouldn't Stack Exchange Norms consider the will of the majority? $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 0:45
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    $\begingroup$ @user2661923 What majority? $\endgroup$
    – DavidPostill
    Commented Dec 3, 2023 at 15:44
  • $\begingroup$ @DavidPostill The vast majority of comments to MathSE posted math problems are hint-comments that attempt to guide the original poster towards attacking the problem themself. If you wish objective evidence, select 50 of these posted questions at random and see for yourself. These comments are not made by ghosts. $\endgroup$
    – user2661923
    Commented Dec 3, 2023 at 16:38

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