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!
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 🙂
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?
You must know (and remember!) a whole lot of integrals, series expansions, special functions, integration techniques, substitutions, differential equations, etc. and be able to combine them to perform the magic he does. Kamal has a huge repertoire and can readily recall the parts when he needs them.
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 TH-cam. It'll be very helpful of you.
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".
sometimes i make that mistake in _14 Minesweeper Variants 2_ when [2P]Product and [2L]Liar are combined
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!
I really appreciate your way of explanation. As a request could you make videos related to tensor calculus
"So, I am horrible at basic arithmetic." Yeah, you just proved that with 1 + 2 = 3 (after factoring out a sqrt(2)), lol. 😂😂😂❤
😂😂😂
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 ,
Always a great night when Kamal uploads.
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 🙂
Very nice. Thanks
Pretty good one. Fan from Sri Lanka ❤🎉
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?
Yeah terribly sorry about forgetting the link😂 it's there now.
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?
You must know (and remember!) a whole lot of integrals, series expansions, special functions, integration techniques, substitutions, differential equations, etc. and be able to combine them to perform the magic he does. Kamal has a huge repertoire and can readily recall the parts when he needs them.
Emm, please, explain me why 1:23 is a partial derrivative!!!
Plz, Plz, Plz, Plz, Plz, Plz, Plz.
Within the integrand, x and α are both variables (not constants), but we're only differentiating with respect to α here.
take a shot every time he writes in the title "A RIDICULOUSLY AWESOME INTEGRAL" 🙂
In 8:25 not "-sec^3"?
@@viktor-kolyadenko it's a CSC function so making vector fall into the 2nd quadrant still makes it positive.
@@maths_505 , csc (x) = 1/sin(x), OK.
(3/4)pi^3
But nothing in the description box?😢
Just fixed it
The thumbnail 😂
title is wrong, should be (0, inf)
What are you guys doing, in college or school.
Mellin transform allert!
Well that was a short one
Solvinfg using Residue Theorem with a keyhole contour....
Those Four poles and a branch cut....
First, once again
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 TH-cam.
It'll be very helpful of you.