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

Подписаться 60 тыс.

Просмотров 16 тыс.

50% 1

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:
www.instagram....
My complex analysis lectures:
• Complex Analysis Lectures
Support my work via patreon:
/ maths505
You can follow me on Instagram for write ups that come in handy for my videos and DM me in case you need math help:
...
My LinkedIn:
/ kamaal-mirza-86b380252
Advanced MathWear:
my-store-ef6c0...
#math #physics #calculus #complex #analysis #passion #hustle #neverstop #stem #stemeducation #advancedmath #teaching #learning #maths505 #mathematics #mathstagram #integral #integration #differential #equations #trigonometry #tutoring #quantum #advancedmath #math #stack #exchange

Опубликовано:

27 окт 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 81

@maths_505 3 месяца назад

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 3 месяца назад

welcome bro! That was a funny yet lucky mistake😂

@vladimir10 3 месяца назад

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

@julianbruns7459 3 месяца назад

Love to see two mistakes cancelling each other out.

@maths_505 3 месяца назад

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

@左括號 3 месяца назад

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 3 месяца назад

One day we'll understand Cleo.

@stefanalecu9532 3 месяца назад

Does Cleo understand us?

@patricius6378 3 месяца назад

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 3 месяца назад

I'm glad this solution is on youtube

@codingforest7442 3 месяца назад

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

@maths_505 3 месяца назад

Thanks mate

@Gekkoulong 3 месяца назад

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

@gmncnr 3 месяца назад

There are so many strategies involved in this!

@vladimir10 3 месяца назад

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

@absurdengineering 2 месяца назад

Our man of integrity delivers! 😅🎉🤩

@xanterrx9741 3 месяца назад

Greatly spended time watching and analyzing

@F-S. 3 месяца назад

The best 1. April joke from FlammableMath

@maths_505 3 месяца назад

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

@MrWael1970 3 месяца назад

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

@trelosyiaellinika 3 месяца назад

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 3 месяца назад

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

@waarschijn 3 месяца назад

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 2 месяца назад

Waarschijnlijk 😢😮

@sharprichard-oq4cf Месяц назад

crazy intergral buff

@sidhantmohanty5256 3 месяца назад

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

@azmath2059 3 месяца назад

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 3 месяца назад

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.

@CM63_France 3 месяца назад

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 3 месяца назад

@@CM63_France been waiting for this all day

@sebastianlopezgiraldo21 3 месяца назад

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 3 месяца назад

Aight

@kingzenoiii 3 месяца назад

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

@subutaibaator6259 3 месяца назад

Finally I found the solution of this integral.

@michaelihill3745 3 месяца назад

That was phenomenal!

@ericthegreat7805 3 месяца назад

This feels like a workout at the gym 😅

@maths_505 3 месяца назад

This is a high intensity leg day🔥🔥

@insouciantFox 3 месяца назад

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

@azmath2059 3 месяца назад

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

@MatthisDayer 3 месяца назад

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

@r.maelstrom4810 3 месяца назад

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 3 месяца назад

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

@r.maelstrom4810 3 месяца назад

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

@maths_505 3 месяца назад

It's cool😂

@nicolascamargo8339 3 месяца назад

Excelente el video

@josephlorizzo8997 3 месяца назад

this was awesome

@JasonLeung-s4c 3 месяца назад

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

@maths_505 3 месяца назад

@@JasonLeung-s4c see the pinned comment

@carlosechacon2560 3 месяца назад

The Goat

@Messigician 3 месяца назад

İmagine this question in final exam of university 💀

@Akhulud 3 месяца назад

This is a whole movie

@maths_505 3 месяца назад

@@Akhulud a cinematic masterpiece

@stefanalecu9532 3 месяца назад

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

@asparkdeity8717 3 месяца назад

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

@nicolascamargo8339 3 месяца назад

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

@maths_505 3 месяца назад

See the pinned comment for a nice laugh my friend.

@50Steaks68 3 месяца назад

What’s your software for writing all this?

@maths_505 3 месяца назад

Samsung notes on my S6 tab

@khengari77 3 месяца назад

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

@maths_505 3 месяца назад

😂😂😂

@Jalina69 3 месяца назад

I like this one

@maths_505 3 месяца назад

I like the pinned comment more😭

@Jalina69 3 месяца назад

@@maths_505))) i should have noticed

@blibilb 3 месяца назад

there has to be a simpler way

@SussySusan-lf6fk 3 месяца назад

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 27 дней назад

Can you write your solution?

@SussySusan-lf6fk 27 дней назад

@@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