The INCREDIBLE Malmsten integral

This was awesome! One of the toughest integrals ever conjured up and so much cool mathematics smashed into one solution development.

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[kingzenoiii]

this integral is zeroeth degree murder

[JoseSanchezLopez-yflo]

man I know you do crazy integrals but this is something else bro this is a murder

[CM_France]

Hi,

"ok, cool" : 2:23, 6:24, 14:54, 20:55, 22:28, 22:57,

"terribly sorry about that" : 11:00, 11:36, 14:36, 18:42, 26:50, 27:17 .

[TheDhdk]

I did not survive... Will try again tomorrow.

[mcalkis]

I do believe it's time to face your destiny and tackle the Borwein integrals.

[stalecu]

Man, I remember when I watched Peyam solve this integral, you did it on 3x speed, this has been just beautiful, we should call you Magician Kamaal because you're pulling tricks left and right

[insouciantFox]

I suffered the little death, in the Shakespearean sense.

[FrankHarwald]

5:00 wouldn't integration by partial sum decomposition make it even simpler because you would be avoiding the infinimal-polynomial product?

[nightmareintegral]

Finnaly legendery integral!
Next Coxeter integrals! 🖤

[D]

“Thank You Math 505” we all said in Unison

[davode]

Early in the morning and I'm watching such an integral instead of going to work!!! 😅

[ashwinbabu]

so early there isn't even a thumbnail

[MohamedElekhtiar--]

I couldn't help but notice that alpha=0 limit exsit in that gorgeous answer, so I did it as a homework and got 1/2ln(e^-γ * pi/2) which is a nice bonus result for a special case of first integral at alpha=0

[aleksandervadla]

Is the integral related to the poisson kernel?

[subutaibaator]

I like Kummer series. Exciting integral!

[euler]

Will come back to this video when my math skills are better

[zachariastsampasidis]

You could say that the quadratic was a known kernel

[felps]

15:09 i just finished calculus I and did not understand most of the things of the video, but i think it is pretty cool watching you solving these integrals

[DOROnoDORO]

The same denominator of the integrand (x² +2xcosα + 1) appears in the result of the sum ∑ Rⁿcos(nθ), for n ≥ 0.
(That is, if we let R=-x and α=θ)
I wonder if this has any significance, of if it could be used to solve this integral in another way.
edit: nevermind, after 4:00 you used a very similar argument

[leroyzack]

This is far harder than the coxeter's integral. What makes it insane is that it's linked to geometric series, Fourier series, Laplace transform. Almost all the craziest analysis stuff where required to solve it. It was really a worthy opponent.