I asked a question (Evaluate the integral $\int_0^\infty \frac{x (\ln(x))^2}{x^4 + x^2 + 1}\text{ d}x$) that I created myself in order to show a particular technique, but apparently people dislike this way of contribution. Is it true that such questions are discouraged?

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    $\begingroup$ I think the problem is with the presentation (and maybe some people didn't read closely enough). The only question you ask is, what is the value of the integral, but it's clear that you know the value of the integral, so it appears that you're not actually asking a question. Maybe if you reworded it to "Here's how I calculated this integral; anyone have another way to do it?" there would be less opposition. Anyway, I wouldn't worry too much, you seem to have gotten a couple of useful answers. $\endgroup$ – Gerry Myerson Jan 10 '15 at 5:28
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    $\begingroup$ For such questions, where you know the answer, or at least one answer, why not use the "Answer Your Own Question" feature? Seems like it's made for such situations. Comments, anyone? $\endgroup$ – Robert Lewis Jan 10 '15 at 6:27
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    $\begingroup$ Math.SE is not a blog. It's not for "I came up with a cool new technique and I want to share it with you guys". And when a post feels that way, it tends to be less welcomed, at least amongst some people. $\endgroup$ – Asaf Karagila Jan 10 '15 at 8:39
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    $\begingroup$ math.stackexchange.com/help/self-answer $\endgroup$ – Najib Idrissi Jan 10 '15 at 10:51
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    $\begingroup$ @Najib Idrissi: that page is very unfortunate. Self-answered questions are not nearly as welcome on this particular site as that page suggests. As Asaf says above, this site is not a blog - it isn't meant for people to say "look what I know". It's meant for questions to which you don't know the answer. Now, if the OP works out an answer after asking the question, that is ideal, and posting that answer is welcome. But a question to which the OP already knows the answer is not a question in a genuine sense. The page you linked ignores this distinction (it was not written by math.SE). $\endgroup$ – Carl Mummert Jan 13 '15 at 11:15
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    $\begingroup$ @CarlMummert My take on this is that, if the question would be OK on its own without being self-answered (it has context etc), then self-answering is OK. Otherwise it's not. Basically, Meelo's answer's first paragraph. $\endgroup$ – Najib Idrissi Jan 13 '15 at 12:18
  • $\begingroup$ @Najib Idrissi: we are looking at two different issues. The issue is not whether it is OK to answer one's own questions - it is certainly OK in certain circumstances. The issue is whether it is acceptable to ask "questions" to which one already knows the answer - which in my mind are not "questions" at all. These are (rightly) discouraged regardless whether the OP answers them or not. $\endgroup$ – Carl Mummert Jan 13 '15 at 17:54
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    $\begingroup$ @CarlMummert I don't see what it changes if you already know the answer, if the question/answer is legitimate and not an obvious reputation grab... What's the difference, from the point of view of someone else, between asking a question and someone else answering, or someone asking and answering, if the Q/A pair is identical? None. $\endgroup$ – Najib Idrissi Jan 13 '15 at 17:57
  • $\begingroup$ @Najib Idrissi: the purpose of the site, though, is the interaction between the asker and answerer. This interaction is absent in immediately self-answered questions, and distorted in "puzzle" questions. The purpose of math.SE is not to serve as a free blogging tool (other StackExchange communities may have different practices, of course.) The idea to make it so is one of the unfortunate legacies of a certain former SE employee. $\endgroup$ – Carl Mummert Jan 13 '15 at 17:59
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    $\begingroup$ @CarlMummert That is one purpose of the site. I can't count how many times I've wanted the answer to something, typed the keyword into google and found the answer here or on MO. Sharing knowledge is also a purpose of the site. $\endgroup$ – Najib Idrissi Jan 13 '15 at 18:23

Your intention of asking a question and then answering it is certainly allowable. However, the usual standards of quality still apply. That is to say, a question which is simply a problem statement (e.g. integrate this by using that) is not only problematic because it will look like homework, but it's also almost never a strong question.

For instance, if someone wants to ask a homework question, I want them to show some effort because then I can know what points they're finding tricky and highlight those in my solution. If someone wants to ask a question out of curiosity, I'd like them to motivate the question somehow.

With your particular question, I think the issue is that the question looks basically like a computation - you gave the technique you wish to use, and a problem tailored to be solved with that technique. It's not terribly open to other answers, and the actual question being solved seems awfully arbitrary - which is problematic, since it means that the question is unlikely to be asked by other people (at least other people who don't already know the answer), and thus the contribution is unlikely to be seen. However, you do seem to have some good question implicit in what you asked - you recognize that your current answer is tedious to put into practice, so it would've been most reasonable to post, as your question, a full solution (or a specific description of your technique, sufficient for someone competent to reconstruct the solution) and to ask if there was a less computation-heavy way to do that.

  • $\begingroup$ Yes, motivate the illustration, perhaps by saying something about what makes the technique worth knowing or interesting. Contour integration involves some art in selecting contours in the complex plane. While a detailed explanation of why this contour works for that integral might best fit in the Answer, mention of your intent (foreshadowing?) would improve the Question for many Readers. $\endgroup$ – hardmath Jan 12 '15 at 16:55

Puzzle Questions are allowed. But, as you see from the comments here, they may be disapproved by many users.

HERE is an example puzzle question I posted a while back. See the disclaimer I put at the top.

  • $\begingroup$ That might explain the seemingly random/unexplained downvotes I've seen on answers to such puzzle questions... $\endgroup$ – Fizz Jan 14 '15 at 18:08

Short answer: yes! We get problems like this all of the time. There are people here that will downvote and vote to close because they do not like simple "Problem Statement Questions" (PSQs). The thinking is that all PSQs come from people who just want free tutoring and are deserving of our scorn. (Such people certainly are.) However, this sort of thinking is robotic; the questions worth answering are hard enough to be obviously not homework.

So perhaps, just to be safe, if you want to pose hard integrals, sums, and the like, that are clearly not homework, maybe spend a line or two explaining how you came across the integral and what your thoughts on a solution might look like. But, in an ideal world, you needn't do that if the problem is hard enough to clearly not be homework.

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    $\begingroup$ Making assumptions about people's motivation and then criticising it is not valid argumentation. I doubt that there are many PSQ-opponents who "robotically" close any question that "shows no effort". Also, it is probably not so much PSQ at work here, but more the line that Gerry and Asaf described in their comments. $\endgroup$ – Lord_Farin Jan 10 '15 at 17:46
  • $\begingroup$ I can't think of a question (much less an integral) that is clearly not homework because of its difficulty. Maybe I've had some unusual and difficult homework in my time. $\endgroup$ – Todd Wilcox Jan 14 '15 at 18:03
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    $\begingroup$ @Lord_Farin: Sorry, but I will push back on that. Yes there are - we have among us those who look at any request to evaluate an integral as something put up by a lazy goodfornothing. I have gotten into repeated arguments about such problems, and have made many requests to reopen. So, no, I am not imagining this. I use the word "robotic" because there is no other way to describe a reason requests to evaluate difficult integrals get repeatedly targeted for closure. $\endgroup$ – Ron Gordon Jan 14 '15 at 18:08
  • $\begingroup$ @ToddWilcox: Take a look through my highest-voted integration answers, for example. $\endgroup$ – Ron Gordon Jan 14 '15 at 18:09
  • $\begingroup$ @Ron I'll take your word for it. Such makes me sad :(. However, regarding your main point, I still firmly contend that it should be promoted, no, mandatory, to provide at least a few lines of context/motivation. They help in locating a question through search engines, gauging difficulty at a quicker glance, identifying handles towards a solution. There's really no downside, except for time, and if a question is worth asking, it is definitely worth those few minutes. (Perhaps we'll have to agree to disagree on this.) $\endgroup$ – Lord_Farin Jan 14 '15 at 18:23
  • $\begingroup$ @Lord_Farin: I don't really disagree with you in spirit - I encourage it (as you can see from this post). But the word doesn't always get out, and sometimes a newbie brings a really interesting challenge here. So perhaps where we disagree is the mandatory thing, just because it is too hard to enforce everywhere. (Experienced users, though, are another story.) As you might be able to tell, these puzzle problems are really what drives a lot of my enjoyment here, so I do take it a little personally sometimes. $\endgroup$ – Ron Gordon Jan 14 '15 at 18:27
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    $\begingroup$ @Ron Well, I suppose we agree then (encouraged for everyone, mandatory for experienced users). But I read the sentiment of your post differently, due to "[P]erhaps, just to be on the safe side, [...] maybe" being a very silk-gloved approach -- hardly encouragement in my book, more like a disappointed realist's take on things. $\endgroup$ – Lord_Farin Jan 14 '15 at 18:33
  • $\begingroup$ @Lord_Farin: You are correct, it does come off that way. $\endgroup$ – Ron Gordon Jan 14 '15 at 18:35

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