# My (deleted) controversial answer to integration problem.

I just noticed that my answer to the Integrating $\int\frac{5}{\ 16 + 9\cos^2(x)}\,dx$ query was deleted.

I also just noticed that I was invited to a chat. Apparently, I got the message to late. Anyway, I think it is reasonable to repeat what I put in the chat, and invite others to criticize/disagree/respond.

I think it is generally important to explain to the OP where he went wrong. In fact, I think that this is often more important than providing the answer.

In this case, as I explained in my answer, which was deleted, I think that the OP (through absolutely no fault of his own) made a serious workflow error. That is, the OP tried to re-invent the wheel, guessing which substitution might conquer the integration problem.

As I indicated in the (deleted) answer, I think that this is almost never a good idea. My objection to the other answers is: (making the large assumption that my perspective is constructive) neither answer indicated (re workflow mistake) where the OP went wrong.

Often, the math teacher (who assigns such a problem) will be lazy or careless and not properly guide the student through the forest of the variety of integration problems which the student might have to tackle.

My answer, which was deleted, was intended to educate the student that sometimes he will be faced with an unfair problem. In that event, the student needs to know how to constructively respond.

user2661923

• I read your answer. You don't have to shout at me now to repeat the details from it. I deleted my comments because you are clearly too angry to listen to what others might have to say. You seem to claim to already know everything there is to know about integration. Good for you. But we at math.se are secular, in that we don't all adhere to the same "bible" of Apostol that you adhere to. Please be tolerant of others, do not throw stones, and others will likely be more tolerant to you, as well. – amWhy Jun 14 '20 at 18:59
• @amWhy For the OP's query, I regard Apostol as deficient. Is there a source that fills the gap? Is there a source that provides a category of integration problems that the OP's query fits into, and describes how to attack that category? – user2661923 Jun 14 '20 at 19:16
• @quid I agree that my meta-post lacked focus. Originally, I made the meta-post because I was late receiving the chat invitation and I thought that it would be discourteous to not fill the gap with the meta-post. Beyond that, I think that quid hit the nail on the head re my disagreement. His meta-post answer indicates that my response to the original posting is not appropriate as an answer. While I will certainly respect this position in the future, I still (privately) disagree because an answer is supposed to show the OP where he went wrong. – user2661923 Jun 14 '20 at 20:26
• Why do you think the chat-invitation was related to this? – quid Jun 14 '20 at 20:45
• @quid because a chat invitation is unusual, because I recognize the controversial nature of my answer to the OP's query, and because my answer was deleted, and because of the timing (re chat invitation when answer deleted). I guessed that a mathSE moderator wanted to chat with me. Also, the chat title had the word integrand in it, which also seemed interesting. – user2661923 Jun 14 '20 at 20:51
• @user2661923 that's the name of the user that invited you. – quid Jun 14 '20 at 21:11
• The discussion of the content of your answer-post is off-topic. It was explained which type of content can go in an answer-post. If specific points remain open, edit the meta-post. This is not the place for chit-chat. (This goes for everybody.) – quid Jun 14 '20 at 23:43
• If your answer had instead gone along the lines of stating, "We should solve these questions by identifying a larger class of questions containing this one with known solutions from some reputable source," then successfully doing that (i.e. finding such a source, reproducing the relevant bits of that source, and applying it to give an answer to the question), I think it would have been well received and your opinion on math would not be the central focus, but would still be present. – Milo Brandt Jun 15 '20 at 15:51
• As an aside (and possibly off-topic, but...): can you please stop using so much bold text? It is distracting, and gives your writing the tone of a rant. It makes you look like you are shouting, which hurts your credibility and distracts from your actual message. – Xander Henderson Jun 15 '20 at 16:19
• @MiloBrandt "If your answer had ...". Your comment seems very reasonable to me. Unfortunately, with the OP's question, I wasn't able to do that, because I don't know of any category of (indefinite) integration questions that the OP's question fits into, that generally yields to the methods used by the other answers given to the OP's question. Therefore, I couldn't find an escape from making my opinion on math the central focus. – user2661923 Jun 15 '20 at 16:38
• @XanderHenderson "can you please stop using so much bold text..." Good point. – user2661923 Jun 15 '20 at 16:39
• @user2661923 If you could not find an "escape" (by citing a credible source and manner to successfully answer the question), you should not have posted solely your opinion on the matter. Answer fields are not designed to host opinions. As Milo stated, had you presented a solution you'd be happy with, in your answer, your answer would not have been deleted. But you didn't; in your answer, you merely scolded others who did, actually have, solutions. If you think there is a better way, then use it. But if you don't know of a better way, don't berate users who at least know a way. to solve. – amWhy Jun 16 '20 at 18:03
• @amWhy As has been pointed out, my use of bold print reads as a rant. Also, I think that your interpretation of my (deleted) answer to the OP's query as scolding is reasonable. In fact, I was using my (deleted) answer to communicate to the OP rather than the others who gave an answer. I was telling the OP where (I thought) he went wrong. If, in fact, the OP has made a workflow error, what is the best way to communicate that to the OP? – user2661923 Jun 17 '20 at 14:32

It seems to me that your answer is mostly a collection of comments. The format of this site is somewhat rigid.

First, there is a question-post that should present a question.

Then, there are answer-posts that should answer the question presented in the question post, and mostly only that.

Reflections and opinions on other answer-posts- or the question-post should be presented, if they are made at all, as comments to the respective post. The should not be presented as an answer-post. Each answer post should mainly try to answer the question presented in the question-post. It is alright to reference existing answer-posts to contextualize one own answer-post in the thread, or to include an aside.

But first and foremost an answer-post must be an actual answer, or at least an attempt at it, to the question presented in the question-post. (It cannot be merely a contribution to the subject in general as an "answer" in a thread of a discussion-board might be.)

If it does not do that it should be removed. This is what happened in this case.

Let me add an afterthought to this. There arguably are some exceptions to the principle above, a culture of those is more developed on sites where this is more relevant. Sometimes somebody might ask a question but in one way or the other one thinks that the person just is not asking the question they should be asking or solving the problem the should be solving.

In such case it can be helpful to answer via a "frame challenge" see

Does Stack Exchange allow for answers which question the validity or stance of the original question?

Another relevant concept is XY problem. See What is the XY problem?

However, these answer should only be given sparingly and when the context makes likely that this is helpful. (In cases of doubt one should solicit this context.)

For the current case, I just do not see this. Somebody doing such integrals is usually doing so because they have to do this as part of a course or alike, and moreover ultimately they usually also have to do so in a constrained environment. Answers of the type: "look it up" or "use a CAS" just are not relevant answers to the underlying problem.

To put this differently, the answer given, could be identically given to hundreds if not thousands of questions that ask how to do some integral or another. Variants of it could be given to tens of thousands of questions.

• "Q: How to compute the determinant of this 3x3 matrix? A: Plenty of software can do that."
• "Q: What are the eignenvalues of of this 3x3 matrix? A: Plenty of software can do that."

And so on. It usually just is not a helpful answer. It might be in select few cases, but if the context clearly suggests it is not, then such an answer should not be given. In cases of doubt, I would put the onus on the person that wants to give such an answer to check if this type of answer is relevant.

• very fair point. I regard your perspective as reasonable. In this (rare) instance, I disagree with your perspective because it suggests that the (other) answers given are constructive. Instead, I regard them as destructive because they teach the OP to tolerate unfair questions. From this perspective, the OP will occasionally be forced to blunder in the dark. The problem with your perspective (in this case) is that it ducks my issue; where did the OP go wrong? ...see next comment – user2661923 Jun 14 '20 at 19:33
• I don't think that the other answers should have been presented without explaining to the OP where he went wrong. In this situation, I think that the OP's mistake was a workflow error. I still think that my response was appropriate as an answer because it addressed where the OP went wrong. I guess I have to ask: do you agree that the OP made a workflow error? If so, isn't an answer supposed to indicate the error? – user2661923 Jun 14 '20 at 19:37
• If you want to comment on other answers use comment-posts on the respective answer-post. – quid Jun 14 '20 at 19:37
• "an answer-post must be an actual answer". I think the post in question has an answer to the question, in the form of a hint (the relevant substitution, together with a reference to relevant literature) that, essentially mechanically, leads to the sought out final expression. – Andrés E. Caicedo Jun 15 '20 at 1:29
• @AndrésE.Caicedo it's not clear if you misread the post (it says they did not find it in Apostol, and the substitution is for a different type of integral). If you did not misread it, I don't think we should allow answers of the form "No doubt it is written in some book, because this vaguely related thing is in this book." In any case this is written in the "answer": "I searched the Apostol book but did not find anything on point re the OP's specific problem." So, they say they did not find anything on point. Does not strike me as an answer. – quid Jun 15 '20 at 3:02
• @AndrésE.Caicedo I agree with quid's interpretation of my original answer. In fact, based on his answer in this meta-post, I agree that my response to the OP's query is inappropriate as an answer. Based on the responses to this meta-post, I seem to be the only one who disagrees with quid's answer in this meta-post. I regard the situation in the original posting as an exceptional case. ... see next comment. – user2661923 Jun 15 '20 at 4:03
• @AndrésE.Caicedo It seems to me that comments are a way of communicating with the person who gave an answer, while a separate answer is a way of communicating directly with the OP. Furthermore, I also think that "long-winded comments" (if on point rather than a rant) are easier to decipher when couched as an answer. I think that there are two core issues that should be considered: (1) Did the OP (through no fault of his own) make a serious workflow mistake? (2) If so, what is the best way to communicate this directly to the OP. ...see next comment. – user2661923 Jun 15 '20 at 4:07
• @AndrésE.Caicedo Obviously, my own opinion (which is all it is) on these questions compelled me to provide the answer that I did to the OP's original query and to continue to disagree with quid's answer in this meta-post. As I indicated to quid, unless I am told differently, I will abide by his answer in the future. I continue to invite anyone to consider the two core questions and let me know what they think. – user2661923 Jun 15 '20 at 4:10
• @user2661923 I added some discussion of what you point out. I agree in principle that this can happen. But the specific case does not strike me as exceptional. There are so many such questions. It seems to me you could have given the exact same answer to many other questions. I understand that maybe you felt the urge to say this once. (I even somewhat agree with the substance of your argument.) But globally we cannot leave such answers up. In the end we'll have thousands and thousands. – quid Jun 15 '20 at 14:44