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Martin Sleziak
Martin Sleziak
11:23
2
Q: Why is ${22\over7}-\pi =\int_0^1{(x-x^2)^4\over1+x^2}dx$

user189728Is this relationship purely an example of a mathematician searching for an equation that satisfies it, or is there a deeper, (possibly geometric), reason?

integration pi
I'm pretty sure this question has been asked before on here... — Frank W. 6 hours ago
@FrankW. I know of a version on MO: mathoverflow.net/questions/67384/… (this is not to say there is none here; only that I know that one) — quid ♦ 13 mins ago
in CRUDE, 12 mins ago, by Martin Sleziak
@quid Approach0 finds a few posts with the same integral, this question is almost a duplicate: Calculus Question: $\int_0^1\frac{(x-x^2)^4}{1+x^2}dx$
in CRUDE, 2 mins ago, by Martin Sleziak
And you can probably find some other questions if you try different forms of this integral, like in this search: https://approach0.xyz/search/?q=%24%5Cint_0%5E1%7B%5Cfrac%7Bx%5E4(1-x)%5E4%7D%7B‌​1%2Bx%5E2%7D%7Ddx%24&p=1
in CRUDE, 2 mins ago, by Martin Sleziak
Anyway, this is more of a topic for another chatroom.
So here are the ones I found so far - not counting the questions already closed as duplicates:
783842: Calculus Question: $\int_0^1\frac{(x-x^2)^4}{1+x^2}dx$
1450910: Shortest method for $\int_{0}^{1}\dfrac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}$
1614676: Creative way for $\int _0 ^1 \frac{x^4 (1-x)^4} {x^2 +1} {\rm d}x$
2084526: Evaluating $\int_0^1 \frac{x^4 (1-x)^4}{1+x^2} dx$
I would not be surprised if somebody finds a few more questions about the same integral.
 
6 hours later…
Wei Zhong
Wei Zhong
17:42
@Sil Right, crawling does take a huge amount of time, even if I am doing it in my lab on campus where Internet speed is fast. In terms of replace_canonical_tex function, I have replied to you on Github, it seems we need to add them back, I will do it now. And your message here indicates you get that set of rules in your replace_canonical_tex function by running through your experiment, so it is based on your experience I guess?

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