Solving the hardest integral on math stack exchange (cleo's monster integral)

Cleo'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:
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[@maths_505]

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]

welcome bro! That was a funny yet lucky mistake😂

[@vladimir10]

Umm... Thanks for that correction Couldn't sleep because of that last night But you made my morning :)

[@julianbruns7459]

Love to see two mistakes cancelling each other out.

[@maths_505]

@@julianbruns7459 I love the fact that the better I get at advanced math, the worse my basic math skills become.

[@左括號]

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]

One day we'll understand Cleo.

[@stefanalecu9532]

Does Cleo understand us?

[@patricius6378]

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]

I'm glad this solution is on youtube

[@F-S.]

The best 1. April joke from FlammableMath

[@maths_505]

And here I am solving it for real I mean for complex😎

[@vladimir10]

Mind-blowing and breathtaking Watched it on x2 because of the length and it was awesome

[@gmncnr]

There are so many strategies involved in this!

[@asparkdeity8717]

I’m watching this at 3am on the day of our general election - something is most definitely wrong with me

[@Gekkoulong]

Incredible integral, still unbelieable that it comes out to be this nice

[@codingforest7442]

Thanks, I really enjoyed the process of solving this integral, You are one of the reasons behind my love for math...

[@maths_505]

Thanks mate

[@absurdengineering]

Our man of integrity delivers! 😅🎉🤩

[@carlosechacon2560]

The Goat

[@Messigician]

İmagine this question in final exam of university 💀

[@ericthegreat7805]

This feels like a workout at the gym 😅

[@maths_505]

This is a high intensity leg day🔥🔥

[@blibilb]

there has to be a simpler way

[@insouciantFox]

My literal reaction: "What is this unholy beast on my floor?"

[@trelosyiaellinika]

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]

Well this one took me 2 days so it'll be a while before I come up with something else 😂

[@sharprichard-oq4cf]

crazy intergral buff

[@waarschijn]

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.

[@wqltr1822]

Waarschijnlijk 😢😮

[@sebastianlopezgiraldo21]

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]

Aight

[@CM63_France]

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]

@@CM63_France been waiting for this all day

[@sidhantmohanty5256]

Ah, yes, the legendary integral solved by Ron Gordon. Great integral.

[@MatthisDayer]

i saw it coming the second you wrote down sqrt(5)

[@azmath2059]

Hard to follow in some parts, but what an amazing result.

[@mau9639]

😭

[@niom9446]

holy shit

[@MrWael1970]

Very interesting monster integral. Thank you for your fruitful effort.

[@xanterrx9741]

Greatly spended time watching and analyzing

[@JasonLeung-s4c]

how did the fraction in natural log simplify to (1 - αsin(x)) at 8:52

[@maths_505]

@@JasonLeung-s4c see the pinned comment

[@khengari77]

Trying to understand why I should buy a new phone was harder than the problem itself 😂😂😂😂

[@maths_505]

😂😂😂

[@subutaibaator6259]

Finally I found the solution of this integral.

[@nicolascamargo8339]

In 7:51 shouldn't it be (2-α*sen(t))(2-β*sen(t)) since (1+t)(1-t)=2?

[@maths_505]

See the pinned comment for a nice laugh my friend.

[@SuperSilver316]

More 30 minute long videos

[@kingzenoiii]

19:34 definitely the best reason to buy a new phone 😂😂

[@SussySusan-lf6fk]

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

[@aryan-oe4ep]

Can you write your solution?

[@SussySusan-lf6fk]

@@aryan-oe4ep actually the same as his but I used this property int - c to c, f(x) dx = int 0 to c, (f(x) +f(-x)) dx This is it... The rest is similar

[@romanvolotov]

too difficult for me, sorry

[@IshayuG]

Oi, don’t judge!😂

[@r.maelstrom4810]

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]

That was just the integral function defined to apply Feynman's trick.

[@r.maelstrom4810]

@@maths_505 My bad. I should have waited longer for the moment you apply the result in the video

[@maths_505]

It's cool😂

[@50Steaks68]

What’s your software for writing all this?

[@maths_505]

Samsung notes on my S6 tab

[@michaelihill3745]

That was phenomenal!

[@Tosi31415]

i smashed my phone, can you buy me a new one?

[@maths_505]

@@Tosi31415 need more patreon supporters for that 😭😭

[@mikecaetano]

Heavy duty!

[@ubncgexam]

🎉🎉 Abs(a*mAz/i+NG) 😂😂👍🏼😎

[@nicolascamargo8339]

Excelente el video

[@josephlorizzo8997]

this was awesome

[@Akhulud]

This is a whole movie

[@maths_505]

@@Akhulud a cinematic masterpiece

[@stefanalecu9532]

​@@maths_505 you'd have multiple Oscars if we took into account all your videos (maybe not the bad accents)

[@Jalina69]

I like this one

[@maths_505]

I like the pinned comment more😭

[@Jalina69]

​@@maths_505))) i should have noticed

[@gesucristo0]

🐐

[@mbaye830]

Far beyond my tiny level i am genualy terrified 💀😥

[@azmath2059]

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]

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.

[@arkadelik]

final boss