A RIDICULOUSLY AWESOME INTEGRAL: int (0,infty) ln^2(x) (1+x^2)/(1+x^4)

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lmao I laughed so hard when I saw the sqrt(2) + 2sqrt(2) = sqrt(2)*(1+sqrt(2)). I thought to myself "nah...not again".

tirterra

I love how you make tough integrals look like child’s play, but basic arithmetic is the hardest part of the video!!! Peak irony! This is your funniest video yet!

darthTwin

I really appreciate your way of explanation. As a request could you make videos related to tensor calculus

astrospecies

"So, I am horrible at basic arithmetic." Yeah, you just proved that with 1 + 2 = 3 (after factoring out a sqrt(2)), lol. 😂😂😂❤

Grecks

When we change ln^2(x) into ln^(2n)(x) we obtain the closed form integral I(n) = (-1)^n*4^n*pi^(2n+1)*sqrt(2)* ( HurwitzZeta(-2n, 1/8) - HurwitzZeta(-2n, 5/8) ) for n an integer ge 0 🙂

DD-cend

Hi,

2:58 : awesome!

6:15 : it's 3 sqrt 2 instead of sqrt 2 ( 1 + sqrt 2 ) . (fixed later).

"ok, cool" : 0:15, 2:19, 5:10,

"terribly sorry about that" : 1:21, 3:16, 5:32,

CM_France

Always a great night when Kamal uploads.

mcalkis

Please send me the link to the integral 2:50, integrate (0, infinity) x^(s-1)/(1+x^k), thanks a lot

daniello

Could you please provide a link to your derivation of the definite integral at 2:45? It looks like it is related to the reflection formula for the Gamma function, isn't it?

Grecks

Pretty good one. Fan from Sri Lanka ❤🎉

sundaresanabishek

How much math must you know to be able to solve so many integrals like this?? Or are ways of solving them always repeating after a lot of practice?

SanAleksiusII

Emm, please, explain me why 1:23 is a partial derrivative!!!
Plz, Plz, Plz, Plz, Plz, Plz, Plz.

leonardobarrera

Solvinfg using Residue Theorem with a keyhole contour....
Those Four poles and a branch cut....

vascomanteigas

take a shot every time he writes in the title "A RIDICULOUSLY AWESOME INTEGRAL" 🙂

ELKCreativist

What are you guys doing, in college or school.

Dharun-gefo

Hey Kamal, can you please give a shout-out to the channel, "The Hidden Library of Mathematics". It's more theory oriented but in my opinion these are some of the best lectures on YouTube.
It'll be very helpful of you.

deviLOfHELLsKitchen

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