Evaluating an absolute Monster - Coxeter's Integral

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  • เผยแพร่เมื่อ 8 ก.พ. 2025
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    Ahmed's Integral: • A Savage Integral! Eva...
    Arctan Int: • Integral 1/(x^2+1) und...
    Outtake PFD: • Behind the Meme: Parti...
    There we go! Let us tackle this absolute bad boi today! This has been my longest video session ever an is atm the longest video on this very channel! Enjoy the show :) I tried my best explaining everything as good as possible =)
    Twitter: / flammablemaths
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    Visit my website! =)
    mathable.me/

ความคิดเห็น • 240

  • @quahntasy
    @quahntasy 6 ปีที่แล้ว +525

    43 minutes of monster slaying.
    Am I in a dream.

    • @tgeofrey
      @tgeofrey 4 ปีที่แล้ว

      Animetor email me at tgeofrey@gmail.com

    • @denverelisha7878
      @denverelisha7878 3 ปีที่แล้ว

      I realize I'm kinda off topic but does anybody know a good place to watch new tv shows online?

  • @gregoriousmaths266
    @gregoriousmaths266 4 ปีที่แล้ว +116

    i see arccos in a derivative, i moan slightly
    i see arccos in an integerahl, i have a mental breakdown

  • @Swimmer7596
    @Swimmer7596 6 ปีที่แล้ว +222

    Lol at "Can we trust the Peano Axioms?"

    • @u.v.s.5583
      @u.v.s.5583 5 ปีที่แล้ว +33

      I don't trust a shady Italian.
      I only trust my accountant. If he tells 2x2=5, then 5 it is.

  • @FICHEKK
    @FICHEKK 6 ปีที่แล้ว +350

    Hey man, I know you love to solve these crazy integrals, but have you ever considered making a series in which you teach people to integrate, starting from the basics and building up the difficulty as the series goes on? Regardless, you are great and keep going!

    • @benmorton3153
      @benmorton3153 4 ปีที่แล้ว +19

      I agree with this statement!!!!!!!!

    • @coycatrett2303
      @coycatrett2303 4 ปีที่แล้ว +30

      that would be flammtastic

    • @AayushBatra
      @AayushBatra 4 ปีที่แล้ว +3

      Yes please make it!!

    • @ericthegreat7805
      @ericthegreat7805 4 ปีที่แล้ว +8

      Yes pls

    • @melaniem2965
      @melaniem2965 4 ปีที่แล้ว +11

      I think he should teach advance integration, but if we’re talking about integrate x^2 + 2, There are many channels for that

  • @parthpawar7837
    @parthpawar7837 6 ปีที่แล้ว +153

    41:15 Ahmed's Integral! Top 10 anime cross overs, that was really surprising

  • @46pi26
    @46pi26 6 ปีที่แล้ว +88

    TH-cam: "Alright Papa I know you're starving so here are 7 ads just make sure you're family friendly"
    Papa Flammy: *skullfucks a monster integral*
    TH-cam: oof

  • @anegativecoconut4940
    @anegativecoconut4940 6 ปีที่แล้ว +91

    There is no nice cancellation in the wild. Papa's just taught this to you.

  • @akshaypr9164
    @akshaypr9164 4 ปีที่แล้ว +24

    Good job! ..Yes you can interchange the integrals due to the tonelli's theorem..notice that your integrant is a positive quantity(luckily!!) and also it turns out to be continuous(very lucky), hence is a measurable function( wow!!) hence you can interchange the integral signs.

  • @SuperSilver316
    @SuperSilver316 4 ปีที่แล้ว +20

    that moment when you you are doing so many transformations, that I forgot what integral we were doing

  • @weerman44
    @weerman44 6 ปีที่แล้ว +18

    Amazing man. Really love this channel

  • @danielesantospirito5743
    @danielesantospirito5743 3 ปีที่แล้ว +5

    I came back to watch this video a second time to "train my attention", trying to watch it from the beginning to the end without losing any passage. It's a very nice and difficult integral, I really admire the fact that you don't use notes, I think I would not be able to remember such a procedure without doing it many times.

  • @neilgerace355
    @neilgerace355 5 ปีที่แล้ว +43

    11:37 No, I can't. This time I would like you to prove 2 x 2 = 4 please.

  • @azmath2059
    @azmath2059 6 ปีที่แล้ว +3

    This is just flamin' unbelievable !! What you are doing here requires great skill and discipline considering that your lecturing from memory without notes or cue sheets. Well done!!

  • @atrimandal4324
    @atrimandal4324 6 ปีที่แล้ว +61

    37:24 :') Good old days of Fappable Maths
    41:15 Wtf dude that was crazier than most crossovers 😍😍
    Hey, random week 2.0 was great

    • @atrimandal4324
      @atrimandal4324 6 ปีที่แล้ว +1

      Flammable Maths Find me one person who didn't 😂😂

    • @fabfin5814
      @fabfin5814 6 ปีที่แล้ว +5

      dem engineer bois already attracted :b

    • @atrimandal4324
      @atrimandal4324 6 ปีที่แล้ว +2

      FabFin Dude, I'm a med student and I'm addicted to Maths partly because of this channel. Show this to a Lib. Arts guy and he'd be attracted too😂😂

    • @Kuratius
      @Kuratius 6 ปีที่แล้ว

      "Cocksetters integral"

    • @fabfin5814
      @fabfin5814 6 ปีที่แล้ว

      Jim Moriarty whatever you want to tell me with that, I agree.

  • @leroyzack265
    @leroyzack265 ปีที่แล้ว +1

    This was an absolute monster and you did a monstrous job. Really I rank this integral as one of the taughest. 🎉🎉
    I really love this one it was awfully amazing.

  • @3manthing
    @3manthing 4 ปีที่แล้ว +7

    My respect for not losing your shit filming this video, calculating stuff in your head all the time.☺

  • @Melanie12047
    @Melanie12047 6 ปีที่แล้ว +48

    40 min of integration MY DREAM CAME TRUE😍😍❤❤

  • @reydavid7300
    @reydavid7300 6 ปีที่แล้ว +8

    I just started the video. This is above 43 minutes log but long time ago I knew a mate that evaluated this integral by exchanging "2cos(x)" for "tcos(x)" the he took the derivative of the whole integral with respect to t, made some cool simplifications then integrated with respect to x, uterly, he integrated with respect to t and found the constant.

  • @bryantwiltrout5492
    @bryantwiltrout5492 5 ปีที่แล้ว +1

    Great pun! “De-phi-ing” I laughed out loud at that. Well done sir!

  • @jfb-
    @jfb- 6 ปีที่แล้ว +5

    You can justify interchanging the integrals by Tonelli's theorem, which allows you to interchange integrals where the integrand is non negative

  • @maximilianmueller4707
    @maximilianmueller4707 6 ปีที่แล้ว +32

    Sometimes your equal sign looks like a minus sign

  • @ClaytonMurzyn
    @ClaytonMurzyn 2 ปีที่แล้ว

    Dude this was sick! Your algebra is crazy

  • @wherestheshroomsyo
    @wherestheshroomsyo 5 ปีที่แล้ว +22

    29:57 literally hand waving argument lol

  • @ManmohanSingh-tv2tb
    @ManmohanSingh-tv2tb 5 ปีที่แล้ว +2

    It really means for me when solution of integral appears after 1 hour.Great

  • @Harkraft
    @Harkraft 3 ปีที่แล้ว

    My god this is the best thing that I ever seen in my whole life cheers to you man

  • @himanshumallick2269
    @himanshumallick2269 6 ปีที่แล้ว +1

    I'm glad you made a video on the first integral posted on that 'artofproblemsolving' page.
    Waiting for more.....

    • @himanshumallick2269
      @himanshumallick2269 6 ปีที่แล้ว

      @@PapaFlammy69 This one:
      artofproblemsolving.com/community/c7h1674162

  • @ritabratanag1821
    @ritabratanag1821 5 ปีที่แล้ว

    Thank you sir for solving one of the best and magnificient integral which finally terminates into the Ahmed integral

  • @didyoustealmyfood8729
    @didyoustealmyfood8729 3 ปีที่แล้ว +2

    bruh when he pulled that ahmed integral out i was like
    *surprised pikachu face*

  • @jemcel0397
    @jemcel0397 6 ปีที่แล้ว +13

    You really showed Math is fun

    • @jemcel0397
      @jemcel0397 6 ปีที่แล้ว

      Flammable Maths always ;)

    • @yogitshankar6348
      @yogitshankar6348 5 ปีที่แล้ว +1

      His style makes it way for interesting

  • @Naaman-e8g
    @Naaman-e8g 3 ปีที่แล้ว +1

    同級生からこの問題を出されて解らず困っていたので助かりました。
    thank you so much!!

  • @hridayansh7682
    @hridayansh7682 6 ปีที่แล้ว +6

    i was like yeah... i can give it a shot "took the paper, writing the question.... mid way of writing question..... No I can't."

  • @adityavarma193
    @adityavarma193 6 ปีที่แล้ว +6

    I've been doing one MIT integration bee integral a day. I'm not able to solve every one, but I seem to be getting better when I analyze the solutions if I didn't know how to do that integral. It's a tough life...

  • @hubomba
    @hubomba 6 ปีที่แล้ว

    That was inspirational. I was in awe of the size of this lad. Absolute unit.

  • @cesaraugustogilacosta5336
    @cesaraugustogilacosta5336 6 ปีที่แล้ว

    Nice integral. It's useful to practice for some calculus tests. Continue like this man.

  • @danieleferretti9117
    @danieleferretti9117 6 ปีที่แล้ว +10

    You can exchange the integral signs because of the Fubini theorem: you are integrating a positive function, so you can do that

  • @purecalcium354
    @purecalcium354 5 ปีที่แล้ว +1

    I don't really know how to integrate properly, but god damn that was fun to watch.

  • @Invalid571
    @Invalid571 5 ปีที่แล้ว +1

    Sees notification,
    clicks on video,
    sees it's 43 mins long,
    closes video.
    Syke, I watched it all!
    XD

  • @dectorey7233
    @dectorey7233 6 ปีที่แล้ว

    Why doesn't this have enough views? This is fire

  • @cafeinst
    @cafeinst 4 ปีที่แล้ว

    This is perhaps the most interesting math channel on youtube.

  • @danrain12345
    @danrain12345 6 ปีที่แล้ว +14

    Honestly I watch so many videos where people pronounce it “zed” that I now do it lmao

  • @danielkirilov8065
    @danielkirilov8065 6 ปีที่แล้ว

    FUUUUU, finallyyy de 40min intigril :^*
    Sugoi papa.

  • @lukamitrovic7873
    @lukamitrovic7873 6 ปีที่แล้ว +9

    HOLY CRAP 45 MINUTES

  • @somealgebraist
    @somealgebraist 6 ปีที่แล้ว +2

    Coxeter got torched. Well done paypay flemmy

  • @TheRedAnvil40
    @TheRedAnvil40 3 ปีที่แล้ว +13

    I have ZERO idea what was going on, yet I watched a 45 min math problem and now I legit feel bad for him. This is WILD.

    • @TheRedAnvil40
      @TheRedAnvil40 3 ปีที่แล้ว +8

      He could have written anything and I would have believed it.

    • @PapaFlammy69
      @PapaFlammy69  3 ปีที่แล้ว +1

      :DDD

  • @ivancheems35
    @ivancheems35 5 ปีที่แล้ว +2

    I watched rick and morty so I could follow every step of this integration papa

  • @brammiddelkamp1861
    @brammiddelkamp1861 4 ปีที่แล้ว +1

    When you realize the nummerical solution is calculated within a minute and gives the same result

  • @dharmanshah1239
    @dharmanshah1239 6 ปีที่แล้ว +4

    Ohh monster boi!!Thank god finally ...

    • @dharmanshah1239
      @dharmanshah1239 6 ปีที่แล้ว

      Ikr..

    • @dharmanshah1239
      @dharmanshah1239 6 ปีที่แล้ว +1

      Jokes apart Jens you are definitely my inspiration to make my own channel in future..Thankyou!!

  • @Cubinator73
    @Cubinator73 6 ปีที่แล้ว +5

    The big f'n square root at 8:55 really made things easier...

  • @parthpawar7837
    @parthpawar7837 6 ปีที่แล้ว +36

    Press F to pay respect.

  • @dgrandlapinblanc
    @dgrandlapinblanc 5 ปีที่แล้ว

    absolutely crazy. Thank you.

  • @Miaumiau3333
    @Miaumiau3333 6 ปีที่แล้ว +10

    my wrist's gonna hurt tomorrow

  • @u.v.s.5583
    @u.v.s.5583 5 ปีที่แล้ว +3

    Papa's theorem. Every function from R to R is integrable in elementary functions.
    Proof: Come on!

  • @michaelempeigne3519
    @michaelempeigne3519 6 ปีที่แล้ว +1

    interchanging the integral signs is called fubini's theorem

  • @Setiny
    @Setiny 4 ปีที่แล้ว +2

    I can’t solve the integral - Panic
    There’s a video about it - Calm
    43:13 - Panic

    • @Sokobansolver
      @Sokobansolver ปีที่แล้ว

      I can't solve the integral - Panic
      There's an online integral calculator with steps - Calm
      "The calculation was aborted because it took too long." - Panic

  • @lukamitrovic7873
    @lukamitrovic7873 6 ปีที่แล้ว +93

    Who dislikes this wtf?

    • @Gold161803
      @Gold161803 6 ปีที่แล้ว

      If I were to dislike it, it would be because of the ridiculous number of ad breaks.

    • @ifteharulhaque2600
      @ifteharulhaque2600 6 ปีที่แล้ว +5

      @@Gold161803 it's a 40 min vid so it's fair

    • @Gold161803
      @Gold161803 6 ปีที่แล้ว

      @@ifteharulhaque2600 Not really. Every other 40 minute video I've seen has 2 or 3 ads, and maaaaybe a fourth at the beginning or end

    • @gregoriousmaths266
      @gregoriousmaths266 4 ปีที่แล้ว +2

      hehe 69th like

    • @didyoustealmyfood8729
      @didyoustealmyfood8729 3 ปีที่แล้ว

      papa flammy is gonna haunt
      those who dislike this masterpiece

  • @Czeckie
    @Czeckie 6 ปีที่แล้ว +8

    31:30 pappa, you've interchanged the integrals long before this point even though you didn't write it up.

  • @Saki630
    @Saki630 5 ปีที่แล้ว +11

    Gauss did this for fun and Fermat executed this in 13 steps but could not fit it all into margins in Gauss's book.

    • @grant1390
      @grant1390 ปีที่แล้ว

      That would also involve time travel.

  • @kshitijkayastha
    @kshitijkayastha 6 ปีที่แล้ว +3

    Can you please make videos on solving differential equations using Laplace Transformation (and then inverse Laplace)

  • @ChibiSheepy
    @ChibiSheepy 6 ปีที่แล้ว +1

    The most fabulous 43 minutes of my life

  • @duncanw9901
    @duncanw9901 6 ปีที่แล้ว +2

    At 9:30 I just used the triangle thing. Absolutely no idea what you were doing there lol but I got the same thing :)

  • @Ricocossa1
    @Ricocossa1 6 ปีที่แล้ว +2

    That's the final boss of integrals.

  • @temurson
    @temurson 6 ปีที่แล้ว +4

    Okay Papa, I give up. It is 33:01 and my brain turned off. I think that's too much for me xD By the way, I think you should have had 8/sqrt(3), not 8*sqrt(3) at this point (I am not sure though). Thanks for your sacrifice (I cannot call this video anything else)

    • @temurson
      @temurson 6 ปีที่แล้ว +1

      Apparently, your brain did not last much longer than mine xD 39:55 Papa's machine going offline

  • @strikercompact2847
    @strikercompact2847 6 ปีที่แล้ว

    You know... You mad man. I love u

  • @louisthirion8179
    @louisthirion8179 6 ปีที่แล้ว +3

    Same Spiel down here😂😂 8:18

  • @juli099
    @juli099 6 ปีที่แล้ว

    Increible, fantastico, asombroso......

  • @danielwalker2381
    @danielwalker2381 5 ปีที่แล้ว +6

    4:12 my OCD went crazy x-----------------------x

  • @Sokobansolver
    @Sokobansolver ปีที่แล้ว

    Meanwhile here I am still having not learned how to compute derivatives or antiderivatives of inverse trig functions. This seems like the final boss of integral problems.

  • @JohnAbreu17
    @JohnAbreu17 5 ปีที่แล้ว

    I'm loving this organized chaos.

  • @George-ij2gm
    @George-ij2gm 3 ปีที่แล้ว

    Whenever you phase in from the left side of the screen, I got lost. 😂😂😂😂

  • @jamez6398
    @jamez6398 6 ปีที่แล้ว

    Holy fucking shit! 45 minutes!!?? Damn... That is one hardcore integral...

  • @CT-pi2gl
    @CT-pi2gl 3 ปีที่แล้ว

    Need to append the Ahmed integral video into one video for completeness!

  • @shimuzeisusu
    @shimuzeisusu 2 ปีที่แล้ว

    At 23:40 shouldn't the upper and lower bounds change with a change in variable from t to \phi

  • @gesucristo0
    @gesucristo0 6 ปีที่แล้ว +2

    Really impressive man...Could you evaluate 1/3 factorial? Using Γ i showed is equal to int from 0 to inf of e^-x^3 but the i don’t know how to continue

  • @shanmugasundaram9688
    @shanmugasundaram9688 6 ปีที่แล้ว +1

    You do this integral in the style as Andrew Wiles solves Fermat's last theorem.There may be easier way of doing this integral.Anyhow the proof is quite interesting.

  • @neb8167
    @neb8167 3 ปีที่แล้ว

    amazing

  • @PuzzleQodec
    @PuzzleQodec 4 ปีที่แล้ว +2

    22:30 So you _think_ you gpt rid of the 3.... but in reality it hid under the pi.

  • @AliBaba-z3t9w
    @AliBaba-z3t9w 5 ปีที่แล้ว

    You are my hero! BTW, are you Australian?

  • @thethug1946
    @thethug1946 5 ปีที่แล้ว

    That was truly a coxeter integral

  • @shimuzeisusu
    @shimuzeisusu 2 ปีที่แล้ว

    Can we really assume cos (t) / sqrt ( 2 - 3 sin^2 (t)) as a constant?

  • @debjitmullick7004
    @debjitmullick7004 5 ปีที่แล้ว

    Such a fascinating video .... But what was the book in your hands 0:19

  • @balakumarank2006
    @balakumarank2006 3 ปีที่แล้ว +1

    Imagine If this integral is in your compulsory 5 mark question 🤪

  • @tszhanglau5747
    @tszhanglau5747 6 ปีที่แล้ว

    Nice way to end this random week. When will be the next random week?

  • @gregoriousmaths266
    @gregoriousmaths266 4 ปีที่แล้ว

    uwu ahmed's integral at the end!
    That was unexpected

  • @michaelempeigne3519
    @michaelempeigne3519 6 ปีที่แล้ว

    at 29:00, you did not put (x^2 + 3 ) in the denominator when doing the substitution of 1 / ( 1 + u^2 )

  • @VALIANT_Electronics
    @VALIANT_Electronics 6 ปีที่แล้ว

    Sometimes it is difficult to understand some steps in your videos, but after investigating I can understand them a little, for this reason I would like to know if there is a list of topics that we need to know in order to fully understand all the steps when you solve those spicy bois and those beach bois integral's in your videos. I am a second semester student of electronic engineering, I know the differential and integral calculus also linear algebra and a little bit of multivariable calculus.
    Greetings from Valledupar-Colombia.
    Thank you

  • @danielfong2315
    @danielfong2315 6 ปีที่แล้ว +4

    next random week when? :'(

  • @shaqramento3238
    @shaqramento3238 6 ปีที่แล้ว

    That's your masterpiece

  • @MagnetThunder3528
    @MagnetThunder3528 6 ปีที่แล้ว

    Sorry I don't understand where the 2x disappears to in the expression at 4:13. Does it just happen to equal 0 through the variable substitutions or is there another explanation?

  • @RieMUisthegoaT
    @RieMUisthegoaT 6 ปีที่แล้ว +1

    Yeeeee
    I'll stick to my calculus 1 exercises for now thx

  • @markos1623
    @markos1623 4 ปีที่แล้ว +1

    Imagine if the camera ran out of battery and he didn't notice...

  • @dagatho
    @dagatho 6 ปีที่แล้ว

    Papa you're insane, how do you come up with this sorcery? Fucking insane

  • @ishaanshrivastava8671
    @ishaanshrivastava8671 5 ปีที่แล้ว

    Did you figure it out?

  • @ricardofranco7419
    @ricardofranco7419 4 ปีที่แล้ว

    Hmm it’s been a while but can we not use complex analysis to do this integral and make it be less steps?

  • @Mot-dh5sx
    @Mot-dh5sx 6 ปีที่แล้ว

    I was watching this at 3 am and accidentally fell asleep while watching. idk

  • @TrickingSeba
    @TrickingSeba 6 ปีที่แล้ว +1

    Oh boiii, look at the length :o

    • @TrickingSeba
      @TrickingSeba 6 ปีที่แล้ว

      so long it hurts :^)

  • @miltonalvarado4155
    @miltonalvarado4155 6 ปีที่แล้ว

    Wow your very wise. Can you recommed some math book???

  • @mithsaradasanayake3211
    @mithsaradasanayake3211 3 ปีที่แล้ว

    Seeing whether this has a complex answers or we could call in quaternions

  • @Idk-hp3oo
    @Idk-hp3oo 6 ปีที่แล้ว +6

    #Hard 2 swallow pills:This Integral.

  • @happyman_smiling
    @happyman_smiling 6 ปีที่แล้ว

    Can we integrate hyperbolic functions

  • @Tomaplen
    @Tomaplen 6 ปีที่แล้ว

    I must have that T-shirt, please tell me what to do