The coolest trig integral!

[@CM63_France]

Hi, "terribly sorry about that" : 2:22 , 5:13 , 10:52 , 12:34 , 14:46 , 16:47 , 17:31 , "ok, cool" : 2:30 , 3:21 , 5:29 , 7:20 , 10:17 , 12:50 .

[@Zetainclination-gs7wg]

okay.... cool

[@leroyzack265]

The fact those series weren't giving log,exp,trig or finite polymials made me think there weren't pretty. Studying them presently just make me understand that Euler too may be discovered the exp function as a series before giving it that cool notation. For those who haven't done advanced maths, those special functions usually look not natural. But when we see that a function is born as a series which is solution to a differential equation, all of them there for become natural. For me the most terrifying of all is the hypergeometric function that has 4 inputs. 😂

[@graham741]

It feels weird to think about the idea that functions born as a series for diff eqs also are born as mappings of sets with certain properties between eachother

[@driesvanheeswijk1633]

Have you ever considered live streaming? You are absolutely phenomenal at improvising from what I can see, and you have charisma and humor. I know we don't get to see the takes that go really, really wrong, but I feel like that doesn't really matter that much. Math streams would be a pretty new idea which might attract a lot of people! Well, regardless, good luck. Thanks for the great videos, man. I love them

[@leroyzack265]

Very violent result. It's cool those monstrous series expansion are denoted with pretty inoffensive letters.

[@maths_505]

@@leroyzack265 😂

[@mcalkis5771]

Taking a break from the advanced math on my computer to see what the advanced math on my phone is doing.

[@maxmoedough6401]

Shout-out to all the Balrogs watching from the deep places of the earth

[@gchu_]

I watch from the depths

[@yurfwendforju]

Just a pleasure watching you do this. It's like a french dude expressing their love to me but the only word I understand is "baguette". I love how these series just turned into those small neat functions. Math really is more like a language than anything else. I think I'll give myself some time studying everything you've done in your video. Defenetly be coming back to this. Great vid! ❤

[@dharunpranay8581]

Wow ! My first 3 favourite functions (gamma, beta, Bessel) used in a single video. But if my 4th function (zeta) involved it would have been more satisfied

[@darksecret965]

That would have madr it complex for sure 😉

[@Damien-d9f]

10:00 or something like that. "π squared which is just π" Let the piplex numbers be of the form p = a+bπ, where a and b are real numbers, π^2 = π, and π =/= 0,1

[@orionspur]

Love them nested functions! Respect. 👊

[@xanterrx9741]

Lovely result , i hope for more videos .

[@aBradApple]

Great video. I have a lot to learn to understand what all of this means. It'll be fun to revisit this afterwards and count up all the "Aha!" moments I have.

[@amoghopprasad8286]

bro just pulls out random greek letter functions and expects us to decipher what it means

[@aliboukhari110]

Excellent, Akhy, very nice integral🙂

[@MrWael1970]

Very interesting solution. Thanks

[@ghkthILAY]

great video as usual,small note though- instead of splitting the integral to 2 and doing the +pi/2 sub and then arguing about symmetry you could have just substituted x -> x/2 and reach the same result

[@Loots1]

i respectfully disagree

[@cdkw2]

well that took a while but it was worth it!

[@maths_505]

Indeed

[@ELKCreativist]

trigg snacc

[@zunaidparker]

Dude, I just got a S24 Ultra and thinking about launching a maths channel focusing on algebra and more fundamental proofs rather than "fun" integrals. What app do you use? I don't see Samsung Notes having the same convenient interface as yours. Thanks man, will keep you posted if I decide to try it.

[@maths_505]

I'd definitely subscribe to that. The Samsung notes app I use is the one for the tablet version so it does look a bit different

[@slavinojunepri7648]

Excellent

[@alipourzand6499]

Terribly sorry about that, but if you have noidea what beta, gamma, Bessel and Struve functions are, either you have nothing to do here or you have to instruct yourself! Great video.

[@sobercohen7486]

wasn't very relevant to my current calculus course but i seemed to enjoy it as much as i could o7

[@maths_505]

Welcome to the channel bro

[@ebw000]

soh cah tuah and trig on that thing

[@emberdied]

I thought u will solve the two summation into a cool constant 😅

[@historicallyaesthetic2899]

Could you possibly use the complex trig functions for this out of curiosity?

[@maths_505]

That could work

[@historicallyaesthetic2899]

@@maths_505 I’m going to kiss you baby girl 😘🎻

[@aravindakannank.s.]

​@@historicallyaesthetic2899💀

[@GeraldPreston1]

epic

[@giuseppemalaguti435]

Visto così,penso che avrò bisogno di 2/3 giorni per la soluzione...ma ci riuscirò

[@sakshampokhrel42]

Hey can you prove, tan(3x)+tan(2x)+tan(x) = tan(3x)*tan(2x)*tan(x)

[@Anmol_Sinha]

Meanwhile me who got (pi-2+2cos1+2sin1) ....

[@trelosyiaellinika]

Extremely beautiful as is your habit! You introduced two special functions I have no idea of... Food for thought and further digging for me... That's intriguing! Thanks! I think you have some discord between your mind on the one hand and your tongue and hands on the other, they are competing and jumping ahead of each other 😂😂 At 3:25 you missed the one half before the Beta function then at 6:15 you corrected it inadvertently and later at 15:25 you had the same conflict, which you realised and corrected immediately... No harm done. I really enjoy your videos Kamal jan. Keep up with the good work!

[@MartinLutherWilliam]

I disagree with the approach... There's indeed a simpler & straightforward solution to this integration problem.

[@txikitofandango]

Maybe it would behave a little better if you integrated from 0 to 2pi

[@aravindakannank.s.]

hi bro

[@maths_505]

Hey mate

[@aravindakannank.s.]

​@@maths_505​ I dosed off while watching After I woke up i continued without even brushing just to question which multiverse I'm in after seeing this 16:04 .For one minute I just stared at the abyss .And asked what??, just to find out it's old school arithmetic error (which initially I thought I did wrong due to aftermath of sleep )