Solving the hardest integral on math stack exchange
Рет қаралды 12,260
Ай бұрынCleo's most famous integral on math stack exchange. It definitely looks like the final boss of integration and the solution development involves a few of my favorite tools so the integration was a wonderful journey indeed.
Rizzy's solution:
pC1moI0buJ...
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@maths_505 Ай бұрын
FUNNY CORRECTION: In the factorisation around the 7:50 mark, the roots of the equation are actually (1+i)/2 and (1-i)/2. The reason it doesn't matter and the result is unaffected is because instead of writing the factorisation as (a-x)(b-x), I went for (1-ax)(1-bx) which essentially means I "factored" out a and b leaving behihd their reciprocals as coefficients of x. And the reciprocals of the roots i found are exactly 1-i and 1+i respectively 😂😂😂. Huge shoutout to my buddy on Instagram Naman Sanghi for pointing this out. Thanks mate.
@namansanghi1940 Ай бұрын
welcome bro! That was a funny yet lucky mistake😂
@vladimir10 Ай бұрын
Umm... Thanks for that correction Couldn't sleep because of that last night But you made my morning :)
@julianbruns7459 Ай бұрын
Love to see two mistakes cancelling each other out.
@maths_505 Ай бұрын
@@julianbruns7459 I love the fact that the better I get at advanced math, the worse my basic math skills become.
@user-cj5lf6dk1k Ай бұрын
Worth mentioning that the wrong factoring made you lost a factor of a half, but since you lost this factor for both the numerator and the denominator, this result is unchanged. After all the errors, they still cancel out
@Noam_.Menashe Ай бұрын
One day we'll understand Cleo.
@stefanalecu9532 Ай бұрын
Does Cleo understand us?
@gmncnr 25 күн бұрын
There are so many strategies involved in this!
@patricius6378 Ай бұрын
As a long time Flammy viewer and also that one guy who wrote about Fortnite in your community tab, I didn't even consider my hopes of you doing lengthy beautiful integarahls would be fulfilled by virtue of a solution to this absolute beast we call the 'master of integration' :)
@arunknown2177 Ай бұрын
I'm glad this solution is on youtube
@Gekkoulong Ай бұрын
Incredible integral, still unbelieable that it comes out to be this nice
@vladimir10 Ай бұрын
Mind-blowing and breathtaking Watched it on x2 because of the length and it was awesome
@MrWael1970 Ай бұрын
Very interesting monster integral. Thank you for your fruitful effort.
@xanterrx9741 27 күн бұрын
Greatly spended time watching and analyzing
@F-S. Ай бұрын
The best 1. April joke from FlammableMath
@maths_505 Ай бұрын
And here I am solving it for real I mean for complex😎
@michaelihill3745 Ай бұрын
That was phenomenal!
@codingforest7442 25 күн бұрын
Thanks, I really enjoyed the process of solving this integral, You are one of the reasons behind my love for math...
@maths_505 25 күн бұрын
Thanks mate
@waarschijn Ай бұрын
24:47 For any analytic function that is real on the real axis, we have f(z*) = f(z)*, where asterisk means complex conjugate. This is because the coefficients of the power series are real.
@subutaibaator6259 Ай бұрын
Finally I found the solution of this integral.
@trelosyiaellinika Ай бұрын
This time you really blew me out! I've got scratch marks on my head now... :D I was like OK, let's see what infinite series we will introduce or when will the Gamma, Beta pop up... The complex world was a pleasant surprise... Especially the introduction of the I(α) was genius! It really needs a good eye and long experience to be able to come up with a "reverse engineered" solution like that. I will have to go over this integral multiple times to be able to really digest and appropriate it. I wonder what other approaches there may be. It would be VERY interesting if you come up with a different method and make a video on it when you find the time... In any case, a great THANKS for this. I really enjoyed it.
@maths_505 Ай бұрын
Well this one took me 2 days so it'll be a while before I come up with something else 😂
@nicolascamargo8339 Ай бұрын
Excelente el video
@sidhantmohanty5256 Ай бұрын
Ah, yes, the legendary integral solved by Ron Gordon. Great integral.
@josephlorizzo8997 Ай бұрын
this was awesome
@insouciantFox Ай бұрын
My literal reaction: "What is this unholy beast on my floor?"
@kingzenoiii Ай бұрын
19:34 definitely the best reason to buy a new phone 😂😂
@sebastianlopezgiraldo21 Ай бұрын
Amazing, hey bro couuld you make a video explaining the Maxwell equations, I know there are a lot of videos about that but I like how you explain
@maths_505 Ай бұрын
Aight
@carlosechacon2560 Ай бұрын
The Goat
@ericthegreat7805 Ай бұрын
This feels like a workout at the gym 😅
@maths_505 Ай бұрын
This is a high intensity leg day🔥🔥
@azmath2059 Ай бұрын
Hard to follow in some parts, but what an amazing result.
@MatthisDayer Ай бұрын
i saw it coming the second you wrote down sqrt(5)
@mbaye830 Ай бұрын
Far beyond my tiny level i am genualy terrified 💀😥
@azmath2059 Ай бұрын
To fully understand what you did, i had to watch this the second time and take notes. This is truly an unbelievable solution!
@maths_505 Ай бұрын
You should check out the one I linked in the description box. It's a bit more generalized and the evaluation of inverse sine functions is alot cooler.
@asparkdeity8717 Ай бұрын
I’m watching this at 3am on the day of our general election - something is most definitely wrong with me
@mikecaetano Ай бұрын
Heavy duty!
@Jalina69 Ай бұрын
I like this one
@maths_505 Ай бұрын
I like the pinned comment more😭
@Jalina69 Ай бұрын
@@maths_505))) i should have noticed
@Messigician Ай бұрын
İmagine this question in final exam of university 💀
@JasonLeung-s4c Ай бұрын
how did the fraction in natural log simplify to (1 - αsin(x)) at 8:52
@maths_505 Ай бұрын
@@JasonLeung-s4c see the pinned comment
@Akhulud Ай бұрын
This is a whole movie
@maths_505 Ай бұрын
@@Akhulud a cinematic masterpiece
@stefanalecu9532 Ай бұрын
@@maths_505 you'd have multiple Oscars if we took into account all your videos (maybe not the bad accents)
@gesucristo0 Ай бұрын
🐐
@r.maelstrom4810 Ай бұрын
At 9:00 How on earth did you get the cancellation of the terms of the numerator and denominator to arrive at I(a)=Int (1/(sinx))*ln(1-asinx)dx)?
@maths_505 Ай бұрын
That was just the integral function defined to apply Feynman's trick.
@r.maelstrom4810 Ай бұрын
@@maths_505 My bad. I should have waited longer for the moment you apply the result in the video
@maths_505 Ай бұрын
It's cool😂
@nicolascamargo8339 Ай бұрын
In 7:51 shouldn't it be (2-α*sen(t))(2-β*sen(t)) since (1+t)(1-t)=2?
@maths_505 Ай бұрын
See the pinned comment for a nice laugh my friend.
@blibilb Ай бұрын
there has to be a simpler way
@50Steaks68 Ай бұрын
What’s your software for writing all this?
@maths_505 Ай бұрын
Samsung notes on my S6 tab
@khengari77 Ай бұрын
Trying to understand why I should buy a new phone was harder than the problem itself 😂😂😂😂
@maths_505 Ай бұрын
😂😂😂
@CM63_France Ай бұрын
Hi, "terribly sorry about that" : 1:43 , 1:49 , 4:35 , 15:50 , 17:20 , 20:54 , 24:01 , 24:13 , 27:46 , "sorry about that" : 10:28 , 11:38 , "ok, cool" : 2:03 , 2:41 , 4:17 , 6:17 , 7:46 , 15:05 , 21:32 , 22:21 .
@maths_505 Ай бұрын
@@CM63_France been waiting for this all day
@niom9446 Ай бұрын
holy shit
@SussySusan-lf6fk Ай бұрын
It's not very hard. I too solved it exactly this way. Just that I used king's symmetric rule and changed limits from ( - 1 to 1) to( 0 to 1) and solved this int 0 to pi/2, 2/sinx ln{ (2sin^2 x + 2sinx +1)/(2sin^2 x - 2sinx +1)} dx
@IshayuG Ай бұрын
Oi, don’t judge!😂
@SuperSilver316 Ай бұрын
More 30 minute long videos
@ubncgexam Ай бұрын
🎉🎉 Abs(a*mAz/i+NG) 😂😂👍🏼😎
@romanvolotov Ай бұрын
too difficult for me, sorry
@Tosi31415 Ай бұрын
i smashed my phone, can you buy me a new one?
@maths_505 Ай бұрын
@@Tosi31415 need more patreon supporters for that 😭😭
@arkadelik Ай бұрын
final boss
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