Ahmed's Integral - An Elementary Approach 

15:13 You'll write great math books one day.

"I just love 69 so much." --flammablemaths,2018

Elementary, my dear papa flammy. Nice integral. Can you do more integrals with complex analysis?

12:12 Well, obviously this 'abomination' converges. For zero it is finite, and as u approaches infinity, the integrand approaches something/u^3, which converges, and this something goes to zero, too. The proof that this integral equals π^2/96 is trivial and left as an exercise for the inclined viewer. Also, I'd like to point out that the 'abomination' equals to ζ(2) divided by 16.

“Elementary approach” 1 second into video: double integral

I shidded and farded

The Integrals be like: "Daddy, please interchange us" xD. Also when you're attuned to you speaking nearly the entire video, the part which is almost silent is a bit weird. But no criticism here, great video as always.

I'm genuinely impressed at how good you are at solving integrals.

4:00 You can do that because the integrand is an integrable function over the square [0,1]x[0,1]. If I recall correctly, basically any function of the form f(x)=1/p(x) where p(x) is a polynomial of degree greater than 2 is integrable over [0,K] for K > 0.

Very nice solution. I solved this by using Feyman's technic by differentiating the integral of arctan(t*sqrt(x^2+2))/((x^2+1)*sqrt(x^2+1)) because when you differentiate the integrand with respect to t the sqrt(x^2+1) in the numerator and the one in the denominator are cancelled and you can also proceed

8:05 some Flammable ASMR

14:46 “Pause and ponder” well someone discovered 3 blue 1 brown recently

Can you do some double or triple integrals?

What did actually happen with the square over the square root at 5:45?

I didn't even know what this integral was before this video. You explained it really well!

Hi Papa Flammy. I was watching your videos of integrating sinx/x and sin^2x/x^2 and understood pretty much all of it, so I tried integrating sin^3x/x^3 from 0 to infinity. I did 3 successive parametrizations (that’s a hard word to spell) and got an expression that is not in terms of x but I was unable to integrate to get back to the original integral. I’m only 18 so I haven’t done complex analysis or contour integration, and only have a very basic understanding of Feynman’s technique. Any help would be much appreciated. :)

24:42 no you're not hehe ............ 69

What a beast

And I just love 31. Also, it's a prime. Love it now.

You're a fucking beast. Nice.

3:55 Foubini under the assumption that Papa is very Papa

That was fucking incredible

You do something cool, keep going

Just when I thought I know the best way to solve ahmed's integral you made this video🤦‍♂️😂. Amazing bruh

Swiiiit :^} Coolioo :DDD

Flammy and A from math on the exam...great fkin day!

tu me séduis

Papa Flammy, I have always been wanting to ask you this. Why do you scribe the integral sign from bottom to top while a majority of us go the other way (that’s how my teacher taught me).

fuck man now I miss "ano'er video"

lost my shit when he said 69 but wrote 96

What's going on at 6:37? Where's the square of the square root from?

Why does this integral have a name? Does it have some sort of significance?

LEGENDre polynomial

Next vid- £5 solution to Ahmed's integral vs £5000 solution to Ahmed's integral Boi, I saw your paper and wtf you actually fucking used 'succ' :')

Coolio! :p

This number of integral signs almost made me lose no nut november

yapacağın çözümü !!!

Whats ur intro song?

Fucking Saucy

What about plus C

Isn't x²+2+1/t² = (x+1/t)² I feel like that would make the integration easier

At 6:05 you forgot the ^2

Wouldn't the reason you can change the order of integration simply be that x and t and independent?

amazing

I just liked the 420th like omg

Most confusing.

ACHMED - not Ahhhmed!

But it's not an easy problem at all 😶