Solving the hardest integral on math stack exchange

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_]

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.

[patricius]

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' :)

[gmncnr]

There are so many strategies involved in this!

[arunknown]

I'm glad this solution is on youtube

[Gekkoulong]

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

[vladimir]

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

[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.

[MrWael]

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

[F-S.]

The best 1. April joke from FlammableMath

[xanterrx]

Greatly spended time watching and analyzing

[codingforest]

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

[ericthegreat]

This feels like a workout at the gym 😅

[subutaibaator]

Finally I found the solution of this integral.

[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.

[sidhantmohanty]

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

[sebastianlopezgiraldo]

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

[insouciantFox]

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

[kingzenoiii]

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

[azmath]

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

[Messigician]

İmagine this question in final exam of university 💀