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

[@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

[@gmncnr]

There are so many strategies involved in this!

[@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

[@vladimir10]

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

[@absurdengineering]

Our man of integrity delivers! 😅🎉🤩

[@F-S.]

The best 1. April joke from FlammableMath

[@maths_505]

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

[@MrWael1970]

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

[@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 😢😮

[@xanterrx9741]

Greatly spended time watching and analyzing

[@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 😂

[@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.

[@sidhantmohanty5256]

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

[@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

[@azmath2059]

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

[@subutaibaator6259]

Finally I found the solution of this integral.

[@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

[@sharprichard-oq4cf]

crazy intergral buff

[@MatthisDayer]

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

[@ericthegreat7805]

This feels like a workout at the gym 😅

[@maths_505]

This is a high intensity leg day🔥🔥

[@insouciantFox]

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

[@michaelihill3745]

That was phenomenal!

[@blibilb]

there has to be a simpler way

[@asparkdeity8717]

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

[@Messigician]

İmagine this question in final exam of university 💀

[@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😂

[@kingzenoiii]

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

[@carlosechacon2560]

The Goat

[@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

[@nicolascamargo8339]

Excelente el video

[@josephlorizzo8997]

this was awesome

[@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

[@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)

[@khengari77]

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

[@maths_505]

😂😂😂

[@Jalina69]

I like this one

[@maths_505]

I like the pinned comment more😭

[@Jalina69]

​@@maths_505))) i should have noticed

[@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.

[@50Steaks68]

What’s your software for writing all this?

[@maths_505]

Samsung notes on my S6 tab

[@niom9446]

holy shit

[@mikecaetano]

Heavy duty!

[@mbaye830]

Far beyond my tiny level i am genualy terrified 💀😥

[@SuperSilver316]

More 30 minute long videos

[@gesucristo0]

🐐

[@mau9639]

😭

[@ubncgexam]

🎉🎉 Abs(a*mAz/i+NG) 😂😂👍🏼😎

[@romanvolotov]

too difficult for me, sorry

[@IshayuG]

Oi, don’t judge!😂

[@Tosi31415]

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

[@maths_505]

@@Tosi31415 need more patreon supporters for that 😭😭

[@arkadelik]

final boss