The Easiest Integral on YouTube

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 1.3K

  • @blackpenredpen
    @blackpenredpen  6 ปีที่แล้ว +639

    OK, I checked the answer and it was correct! th-cam.com/video/mUXdgY5MeEg/w-d-xo.html
    Happy New Year!!!

    • @notnilc2107
      @notnilc2107 6 ปีที่แล้ว +8

      I approve.

    • @alexsanders7303
      @alexsanders7303 6 ปีที่แล้ว +2

      Lol, just finished the vid and relaised this

    • @marziyaali7962
      @marziyaali7962 5 ปีที่แล้ว +1

      Oh god my maths test is on 1st Aug and I haven't prepared for it yet...... integrals is also in test!😢😢😢

    • @pongwang9893
      @pongwang9893 5 ปีที่แล้ว +1

      thanks , the integral is really amazing. so intelligent.
      Mathematics is deeply bottomless, and probability and statistics are more difficult to understand.
      Gamma distribution, chi-square distribution, is so hard to understand.

    • @sahlileila6382
      @sahlileila6382 5 ปีที่แล้ว

      i really need your help to intigrate this for me i really need it ----- x-1*sqrt.2x-x*2
      /x+1

  • @wellbangok8959
    @wellbangok8959 7 ปีที่แล้ว +4963

    Somewhere out there, a professor is gonna watch this video and make this problem a test question. RIP.

    • @davidkippy101
      @davidkippy101 7 ปีที่แล้ว +153

      Sheev Palpatine Saw the comment, liked for the name

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +490

      Sheev Palpatine I just had to pin this comment.

    • @levi4328
      @levi4328 7 ปีที่แล้ว +147

      oh no, don't give them ideas

    • @Mathemusician97
      @Mathemusician97 7 ปีที่แล้ว +105

      Sheev Palpatine that would be acceptable if that was an extra credit question where if you get it right you get full credit for the exam

    • @神-w1y
      @神-w1y 7 ปีที่แล้ว +29

      Sheev Palpatine did you ever hear the tragedy of darth plagueis the wise?

  • @BT7M
    @BT7M 7 ปีที่แล้ว +2786

    You know it's a hard problem when he has to use 3 colors

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +200

      BT7M yup

    • @isaacormesher2851
      @isaacormesher2851 7 ปีที่แล้ว +206

      blackpenredpenbluepen

    • @Anonymous_Poetry
      @Anonymous_Poetry 4 ปีที่แล้ว +28

      This is not hard prblm we indians take 30 sec to solve this

    • @booga9584
      @booga9584 4 ปีที่แล้ว +2

      @@g.peloni3694 none cause we never and then we're like wtf are we doing.

    • @midhun.m4963
      @midhun.m4963 4 ปีที่แล้ว +1

      @@g.peloni3694 uff...😂I'm also An Indian I'm a Calculus Lover too...

  • @AviMehra
    @AviMehra 7 ปีที่แล้ว +2240

    Check the answer by differentiation

  • @yoavcarmel1245
    @yoavcarmel1245 7 ปีที่แล้ว +511

    8:15 *erases that additional line*
    ohh god thank youu

  • @rileywells3045
    @rileywells3045 7 ปีที่แล้ว +343

    This is probably the most fun I've ever had watching a video about integrals! It was a long journey, but it was worth every second. Thankyou for such a great video!

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +19

      Riley Wells my pleasure!!!!

    • @leif1075
      @leif1075 ปีที่แล้ว

      @@blackpenredpen But why on earth would you do that second substitution at all? Isn't there another way maybe more intuitive..like integration by parts Ibwas thinking..Hope you can respond when you can.

  • @friendofjim
    @friendofjim 7 ปีที่แล้ว +960

    I don't want you to check your answer by differentiation. I want you to integrate your answer :D

  • @flansterr
    @flansterr 7 ปีที่แล้ว +514

    I think you did a step wrong somewhere, please differentiate it to check.

  • @davidkippy101
    @davidkippy101 7 ปีที่แล้ว +546

    You're going from blackpenredpen to 3blue1brown

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +179

      How so? His vids are way cooler

    • @Number3pt14
      @Number3pt14 7 ปีที่แล้ว +75

      Because this is really REALLY complicated yet you manage to explain it so well. Its cool at the same time

    • @davidkippy101
      @davidkippy101 7 ปีที่แล้ว +52

      blackpenredpen Because of the color markers you are using

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +95

      blackpenredpen and sometimes blue : )

    • @NoNameAtAll2
      @NoNameAtAll2 7 ปีที่แล้ว +29

      blackpenredpenbluepengreenpen

  • @natalieeuley1734
    @natalieeuley1734 7 ปีที่แล้ว +98

    I love this. Great example of when to actually use partial fractions, too. I'm adding this channel to my list of favorite math channels! 🤓🤓🤓

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +9

      Natalie Euley thank you Natalie!

  • @shakirahsanromeo7863
    @shakirahsanromeo7863 7 ปีที่แล้ว +410

    I fear you may run out of substitute variables one day :P

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +84

      Shakir Ahsan Romeo probably. Next I will use alpha, beta

    • @iconoptixx
      @iconoptixx 6 ปีที่แล้ว +71

      *creates new alphabet after using all latin, greek, cyrillic, hebrew and arabic letters*

    • @Queenhideyxo
      @Queenhideyxo 6 ปีที่แล้ว +11

      Evolution can you give me more letters for my substitions into different integral worlds?
      Sure blackpenredpen
      ACTUALLY USES OLD LETTERS FOR SUBSTITUTIONS LIKE A BOSS

    • @arnavanand8037
      @arnavanand8037 5 ปีที่แล้ว +12

      After that start using ♤♡◇♧¤▪☆

    • @hamiltonianpathondodecahed5236
      @hamiltonianpathondodecahed5236 4 ปีที่แล้ว +7

      How about हिन्दी

  • @andresvivas2814
    @andresvivas2814 7 ปีที่แล้ว +791

    when you say "please do not ask me to check the answer by diferentiation", I'm pretty sure you were really thinking "please ask me to check the answer by diferentiation" ... So, in order to please you..... Would you check the answer by diferentiation???? Please :)

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +182

      lol! I am waiting for some viewers to do it!

    • @manuelbonet
      @manuelbonet 7 ปีที่แล้ว +49

      blackpenredpen We want you to check it by differentiation. It's always easier than the integration, right?

    • @monzur1947
      @monzur1947 7 ปีที่แล้ว +28

      blackpenredpen I proved it using my calculator. Is that good enough?

    • @aysikl
      @aysikl 7 ปีที่แล้ว +10

      scrolled down expecting the comment "check the answer by differentiation" as top or only comment ..
      urs was 3rd and has a bunch of text around it
      internet, you disappoint......
      (altho the expectation ur not meeting, is actually... so in a way.... yay! ....)

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +23

      Maybe?!

  • @bonbonpony
    @bonbonpony 7 ปีที่แล้ว +43

    16:56 Yeah, putting down some TNT on that would definitely help :)
    18:18 It's quite interesting that `1/2` and `√3/2` appear in the completed square, because:
    a) they are the real and imaginary part of the cube root of `-1` that appear in the complex factorization of the denominator;
    b) they are the sine and cosine of the 60° angle at which this cube root lays with respect to the real axis :)
    c) we've got the cube root (of the tangent) in the original integrand.
    21:30 We have to go deeper... :>
    23:52 The dream is collapsing :J

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +7

      Ah!!! I like the pt u made at 18:18... and what u said "The dream is collapsing"

  • @tipoima
    @tipoima 7 ปีที่แล้ว +38

    30:40 "Please, do not ask me to check the answer by differentiation"
    Hey, you should totally check the answer by differentiation!

  • @ianbo1
    @ianbo1 7 ปีที่แล้ว +111

    Worth every second of the watch. Thank you!

  • @maxhaibara8828
    @maxhaibara8828 7 ปีที่แล้ว +567

    I have a challenge for you. Make the generalization of the integral of n-th root of tan x dx

    • @kamarinelson
      @kamarinelson 6 ปีที่แล้ว +50

      I was wondering this myself lol at the beginning of this video. I'm betting it inevitably leads to just letting u= the n-th root of tan(x) and then integrating the resulting rational function using partial fraction decomposition - maybe synthetic division for powers of tangent not = 1 or 2.

    • @kamarinelson
      @kamarinelson 6 ปีที่แล้ว +21

      of course, I'm ignoring any possible trig manipulations ...

    • @eroskuikel9688
      @eroskuikel9688 6 ปีที่แล้ว +16

      This should be easy. Separate tan^n into tan^(n-2) and tan^2 then integrate by parts. Then substitute sec^2-1 for tan^2 and you get a reduction formula. Evaluate integral of tan^2 and that should be enough I guess.(I havent tried this but I think this works for even exponents only.)

    • @eroskuikel9688
      @eroskuikel9688 6 ปีที่แล้ว +2

      Kyro well Oh yeah..

    • @surenmoodley7744
      @surenmoodley7744 3 ปีที่แล้ว +3

      Lol that's sadistic!

  • @JoJoJet100
    @JoJoJet100 6 ปีที่แล้ว +31

    Doctor: You have 31 minutes and eight seconds to live.
    Me: immediately opens this video

  • @azmath2059
    @azmath2059 7 ปีที่แล้ว +11

    Now that is just incredible! By far one of the most difficult integrals I have ever seen and you have solved it so elegantly and so well.

  • @malayagr
    @malayagr 2 ปีที่แล้ว +8

    The second integral can be done without any substitution:
    Multiply and divide by 2 (you can factor out the divide by 2 later, with the final constant distribution):
    (2t+2)/(t²-t+1)
    The derivative of the denominator is 2t-1. So, write the integral as:
    (2t-1+3)/(t²-t+1)
    Split the fraction:
    (2t-1)/(t²-t+1) + 3/(t²-t+1)
    The first one's integral is ln|t²-t+1|. For the second one, complete the square as (t-1/2)²+(√3/2)². The integral is 2√3*invtan((2t-1)/√3).
    Now, distribute the divide by 2:
    1/2*ln|t²-t+1|+√3*invtan((2t-1)/√3).

  • @sethleverett8889
    @sethleverett8889 3 ปีที่แล้ว +30

    Video: “Easiest integral on TH-cam”
    Me: oh that’s nice let’s check it out
    Also video: equation is written very small and 31 minutes
    Me: oh no...

  • @ATeamBrown
    @ATeamBrown 7 ปีที่แล้ว +8

    This couldn't have been uploaded at any time better, I'm just about to fall asleep and I always trance at your videos which makes me go to sleep! Thank you so much! :D

  • @particleonazock2246
    @particleonazock2246 4 ปีที่แล้ว +38

    This problem was soooooo easy! I solved it when I was a foetus. Hats off to this young gentleman realising the foetal power of solving integrals!

    • @lih3391
      @lih3391 2 ปีที่แล้ว +3

      Fetus?

    • @JMZReview
      @JMZReview ปีที่แล้ว +4

      Bro really spelled it with an o 💀

    • @General12th
      @General12th ปีที่แล้ว

      @@JMZReview diarrhoea

  • @Kreighzey
    @Kreighzey 7 ปีที่แล้ว +45

    30:40 differentiASIAN

  • @mr.gentlezombie8709
    @mr.gentlezombie8709 7 ปีที่แล้ว +91

    Now do the integral of (tanx+(tanx)^(1/2)+(tanx)^(1/3)+(tanx)^(1/4)+(tanx)^(1/5)...)

    • @hauler-hx6gw
      @hauler-hx6gw 6 ปีที่แล้ว +1

      Mr. Gentlezombie spoiler alert

    • @aneeshsrinivas9088
      @aneeshsrinivas9088 3 ปีที่แล้ว +2

      this series will diverge, this question doesn't make sense.

    • @mr.gentlezombie8709
      @mr.gentlezombie8709 3 ปีที่แล้ว +1

      @@aneeshsrinivas9088 D'oh!

  • @loganmancuso3791
    @loganmancuso3791 7 ปีที่แล้ว +150

    Ok to the one dislike on the video I want you to post a follow up showing everyone how you do this integral.

    • @nestorv7627
      @nestorv7627 7 ปีที่แล้ว +3

      Mace Jr there is no dislike now

    • @aceeternus4027
      @aceeternus4027 7 ปีที่แล้ว +4

      NestorV S Hhh he couldn't do it.

    • @ZyloSol99
      @ZyloSol99 7 ปีที่แล้ว

      Nah two people did.

    • @busTedOaS
      @busTedOaS 7 ปีที่แล้ว +9

      disliking =/= "i can do better"
      ask any sports fan if you don't believe me.

    • @hamiltonianpathondodecahed5236
      @hamiltonianpathondodecahed5236 4 ปีที่แล้ว

      Now 5³ dislikes

  • @mutenfuyael3461
    @mutenfuyael3461 ปีที่แล้ว +1

    For B in 11:45, I like to multiplie by t in both side, and by going in the limit in +infini, we have 0=A+B

  • @mathematically4761
    @mathematically4761 2 ปีที่แล้ว +9

    I thought he will forget the + C part
    Truly professional to the core
    I am starting to fall in love with math and pens
    And of course our one and only
    *CALCULUS*🥳🥳

  • @dovidglass5445
    @dovidglass5445 3 ปีที่แล้ว +1

    I love how enthusiastic you are! What great videos you make.

  • @stanschimerman
    @stanschimerman 6 ปีที่แล้ว +7

    Fantastic job of explaining every step!

  • @X-3K
    @X-3K 7 ปีที่แล้ว +348

    what about the tan(x) root of tan(x)?

    • @nestorv7627
      @nestorv7627 7 ปีที่แล้ว +42

      I think impossible

    • @aceeternus4027
      @aceeternus4027 7 ปีที่แล้ว +24

      NestorV S I thought you could integrate anything you wanted

    • @RubALamp
      @RubALamp 7 ปีที่แล้ว +96

      Ace Eternus no, there are functions that their integral have no solution. A classic example of this is the function f(x)=e^x^2.

    • @mh-no5it
      @mh-no5it 7 ปีที่แล้ว +59

      Ace Eternus
      Some functions have no elementary anti derivative take x^x for example, you have to settle for a series.

    • @sinistrolerta
      @sinistrolerta 7 ปีที่แล้ว +43

      Gregory House Tecnically there is a solution, but it just can't be expressed in terms of exponentials, polynomials, logarithms etc

  • @void2509
    @void2509 4 ปีที่แล้ว +45

    Imagine doing a test and solving this problem. You did every step right, but you forgot to write plus C

    • @delta2884
      @delta2884 3 ปีที่แล้ว +8

      And professor deducts 1mark for that

    • @invasion8318
      @invasion8318 3 ปีที่แล้ว +6

      @@delta2884 my professor would tear the whole thing and give you 0 ;)

    • @dzlcrd9519
      @dzlcrd9519 3 ปีที่แล้ว +1

      Easier when in France they ask for a antiderivative so you don't have to add +C

    • @好吧-h6k
      @好吧-h6k 3 ปีที่แล้ว

      Calc II + Calc II

  • @andrecouverette
    @andrecouverette 2 ปีที่แล้ว

    Best problem ever!
    Tour de force for methods of integration.
    I counted eight different tricks.
    TI-84 plus showed it correct over:
    -2π

  • @12345678910111213796
    @12345678910111213796 7 ปีที่แล้ว +140

    Can you check the answer by differentiation ?

    • @blackpenredpen
      @blackpenredpen  6 ปีที่แล้ว +19

      Pedro Bessa maybe one day :)

    • @nationalstudyacademykim5030
      @nationalstudyacademykim5030 5 ปีที่แล้ว +1

      Really quick way to check. Takes 30 seconds. Plug in some values the the limit of integration and use fund. Thm of calc p2.

  • @Xperia347
    @Xperia347 7 ปีที่แล้ว +114

    Could you check the answer by differentiation?

  • @eveliohernandez6595
    @eveliohernandez6595 7 ปีที่แล้ว +5

    i never´ ve seen a intgral like this
    . i been watching all your videos and in my opinion is very useful. in other side i want to thank, you videos are helping me to improve my english how you know ,y native language is spanish, but thanks for share it. congrats

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว

      Thank you so much. I am very happy to hear your nice comment! Keep up the good work too!

  • @howtoglobal7901
    @howtoglobal7901 4 ปีที่แล้ว +1

    i just love your videos man... i just want to say that you helped me overcome my fear of integrals.. and your approach to not just this video but all the others are just brilliant.. thank you.

  • @rohitg1529
    @rohitg1529 7 ปีที่แล้ว +19

    Please differentiate this to get back to cuberoot of tan x

  • @joserubenalcarazmorinigo9540
    @joserubenalcarazmorinigo9540 ปีที่แล้ว

    En 6:10. Dentro de las integrales NO se deben mezclar las variables.
    Por eso se llama CAMBIO DE VARIABLES.
    En integrales MULTIPLES sí pueden haber mas de una variable

  • @vj_henke
    @vj_henke 7 ปีที่แล้ว +36

    This channel is now offically a MATH MEME !
    "How about the integral of [fancy variation of sqrt(tan x)] ?" - bprp, you have a long meme carrier ahead...

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +11

      oscarjd74 OH WOW!!!! YOU ACTUALLY DID IT!

    • @vj_henke
      @vj_henke 7 ปีที่แล้ว +3

      NEAT, instant screen saver ^^

    • @caducoelho2221
      @caducoelho2221 7 ปีที่แล้ว +1

      How cool iz dat?! HAHAHAH

  • @hendrickdias8366
    @hendrickdias8366 7 ปีที่แล้ว +1

    Watching this made me very relaxed. You sir deserve a subscribed!

  • @clementtan5004
    @clementtan5004 7 ปีที่แล้ว +112

    here i am watching 30 minutes of math porn and not knowing wtf is going on

    • @kibayuuto6634
      @kibayuuto6634 6 ปีที่แล้ว +17

      Clement Tan isn’t that the case when watching regular porn too?

    • @suyunbek1399
      @suyunbek1399 6 ปีที่แล้ว

      Жиза

  • @DavideCosmaro
    @DavideCosmaro ปีที่แล้ว +1

    25:49 let's all appreciate how his only mistake in the video was using the wrong coloured marker

  • @DreamzAnimation
    @DreamzAnimation 7 ปีที่แล้ว +13

    please check the answer by differentiation

  • @君爵_2045-y7k
    @君爵_2045-y7k ปีที่แล้ว

    15:20 i think we can multiply 2 then having a division before completing the square 2(t+1)-3+3/t*2-t+1=2t-1/t*2-t+1 +3/t*2-t+1,so that we do not need to do substitution with w

  • @BlackFiresong
    @BlackFiresong 7 ปีที่แล้ว +3

    I kept on making mistakes when trying to check this answer by differentiation, and had pledged to keep this video tab open until I had successfully checked it. So pleased to say that I finally got it right today! I can close the tab now. :D

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +1

      BlackFiresong wow nice!!! I will check it one day too.

    • @BlackFiresong
      @BlackFiresong 7 ปีที่แล้ว +1

      Thank you so much for replying! Love your work. :) Please do keep the crazy challenges coming. You have really helped to rekindle my love of Maths!

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +1

      BlackFiresong I am very glad as well!! Thank you for watching my videos :)

  • @vynderma
    @vynderma 4 ปีที่แล้ว

    Glad you enjoyed yourself with that. This is a great review of a lot of techniques.

  • @blackpenredpen
    @blackpenredpen  7 ปีที่แล้ว +7

    He did the derivative!!!!!!!!!!!! Check out Fematika's
    th-cam.com/video/as1vk0IuAHA/w-d-xo.html

  • @MRBYRNO2505
    @MRBYRNO2505 5 ปีที่แล้ว +1

    you are such an amazing teacher you make this advanced stuff seem so easy

  • @philmertens2673
    @philmertens2673 7 ปีที่แล้ว +44

    Please make a video about the nth root of tanx

    • @TheTimeDilater
      @TheTimeDilater 7 ปีที่แล้ว +5

      yes i agree

    • @dicandeo9698
      @dicandeo9698 7 ปีที่แล้ว +3

      Yes, that'd be great! :)

    • @sunriselp849
      @sunriselp849 7 ปีที่แล้ว +5

      I want to see that too

    • @jiaming5269
      @jiaming5269 7 ปีที่แล้ว +4

      tan(nx) ^ (1/n)

    • @angelmendez-rivera351
      @angelmendez-rivera351 7 ปีที่แล้ว +1

      I want to see this too, although I'll try it myself first because it may be possible that it be not expressible in terms of elementary functions or with a finite definite expression.

  • @prollysine
    @prollysine 3 ปีที่แล้ว

    Gratulálok, ez a szinte végig helyettesítéses módszer bemutatta, hol kezdődik az elméleti matematika !

  • @tavishu
    @tavishu 5 ปีที่แล้ว +3

    Great, now integrate (tanx)^1/5

  • @NWSCS
    @NWSCS 7 ปีที่แล้ว +1

    The interesting thing would be a professor taking the solution of that integral and making the class find the derivative maybe as a bonus problem on an exam.

  • @JBaker452
    @JBaker452 7 ปีที่แล้ว +9

    This does turn out to be a monster of an integral "doesn't it" :-)

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +2

      Yea, isn't it?!

    • @JBaker452
      @JBaker452 7 ปีที่แล้ว

      So how does the monster grow in the complex domain?
      I would love to see the secrets in there so that I might apply them to quantum mechanics (and my cool design for a new warp drive model).

  • @enriquevanegas5741
    @enriquevanegas5741 6 ปีที่แล้ว

    Jesus Christ! With this you have won a new follower! Subscribed!

  • @benjaminbrady2385
    @benjaminbrady2385 7 ปีที่แล้ว +4

    I was kind of hoping to see you dancing in celebration chanting "One Take!" at the end

    • @xamzx9281
      @xamzx9281 7 ปีที่แล้ว +1

      who knows maybe its 10th take

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +1

      Notice that I didn't edit this video!

    • @markzero8291
      @markzero8291 7 ปีที่แล้ว +1

      MrQuantum "one take" and "1st take" are different.

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +4

      Mark Zero true. One take for this tho. I think it was my 3rd take bc my intros weren't good enough.

    • @xamzx9281
      @xamzx9281 7 ปีที่แล้ว +1

      Mark Zero k

  • @AdamMajewski-h1h
    @AdamMajewski-h1h วันที่ผ่านมา

    I know this is 5 years later but dont forget to divide the lns. Also for partial fractions you can multiply the denominators on the left side to make it easier. Hope this helps

  • @bonbonpony
    @bonbonpony 7 ปีที่แล้ว +9

    Can you make some videos about the strategies of choosing the right integration technique for different problems?

  • @chessandmathguy
    @chessandmathguy 7 ปีที่แล้ว +1

    very very good video and very satisfying to have a clean solution in the end.

  • @sirfactor
    @sirfactor 7 ปีที่แล้ว +5

    You earned yourself a new sub
    Thanks sir .

  • @meraldlag4336
    @meraldlag4336 ปีที่แล้ว

    I'm so happy to see a "BIG INTEGRALS NO SHORTCUTS" playlist, will watch them all

  • @jeffreycanfield1939
    @jeffreycanfield1939 7 ปีที่แล้ว +44

    I'm worried for you.

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +71

      MistaTwoJeffreyTwenty Yaay
      U should worry about my students

    • @jeffreycanfield1939
      @jeffreycanfield1939 7 ปีที่แล้ว +8

      blackpenredpen oh noooo, show them sympathy please, they don't deserve this!

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +2

      Lol! I am teaching a calc2 class in the fall. We will see!! : )

    • @JorgetePanete
      @JorgetePanete 7 ปีที่แล้ว

      blackpenredpen the next year i will see integrals on our tests and i need a bless from Pitagoras to pass these exams

    • @Metalhammer1993
      @Metalhammer1993 7 ปีที่แล้ว

      if they´re not nice they get this integral on their exam! how about that? or worse sin(x)/x from 0 to infinity (but don´t ask for the steps. that´s overkill. though maybe you can show us that one? i didn´t see a single video on YT about that ntegral i would have understood. and the only idea to even make this possible would be using the mclaurin series of the sine)

  • @KrisEditz29
    @KrisEditz29 5 ปีที่แล้ว +1

    Most elegant integral I've seen so far,thank you sir

    • @ktuluflux
      @ktuluflux 2 ปีที่แล้ว

      Nothing even remotely elegant about this. This is the equivalent of opening a safe by dropping an anvil on it.

  • @ulilulable
    @ulilulable 7 ปีที่แล้ว +3

    This is so great! I wish I still had the "mathematical muscle" to do this myself. Maybe one of these days...

    • @thelegendofme7520
      @thelegendofme7520 3 ปีที่แล้ว +2

      Hey man just checking in, its been 4 years hows that math muscle working out for you? I challenge you to do 3 integrals! You can do it

    • @ulilulable
      @ulilulable 3 ปีที่แล้ว

      @@thelegendofme7520 Aaany day now... ;)

  • @MaximQuantum
    @MaximQuantum 3 ปีที่แล้ว +1

    "The Easiest Integral on TH-cam" = kalm
    *Sees the video length **31:08**" = PANIC*

  • @sunglow9835
    @sunglow9835 6 ปีที่แล้ว +5

  • @kummer45
    @kummer45 2 ปีที่แล้ว

    Standard integrals are square root of tangent x, tangent x elevated to 1/3 and so on like tangent x elevated to 1/4. The exercise gets extremely complicated when we consider powers of 1/5 and so. I think that tangent to the 1/2 and tangent to the 1/3 are fair practice problem for assignments covering almost every technique in integration.
    This is a good exercise for substitution, partial fraction, determinants and the Gauss Jordan elimination method. It has the classical strategies and the knowledge of well known integrals including the logarithmic ones.

  • @AviNash6817
    @AviNash6817 7 ปีที่แล้ว +7

    Good. this is a high level problem in my sheet .

  • @redvine1105
    @redvine1105 7 ปีที่แล้ว

    You're a braver man than I. Damn that's one intense integral.

  • @kylefarias9143
    @kylefarias9143 7 ปีที่แล้ว +13

    do the integral of sqrt(tan(cuberoot(tanx)))

    • @nejlaakyuz4025
      @nejlaakyuz4025 5 ปีที่แล้ว

      Kyle Farias Just use numerical integration on given bounds

  • @klokcotizao224433199
    @klokcotizao224433199 4 ปีที่แล้ว +2

    And my professor is expecting me to solve that in only 10 minutes.

  • @citizenalex1934
    @citizenalex1934 6 ปีที่แล้ว +4

    "When in doubt, use horseshoe mathematics."

    • @craftbuzzwonky4752
      @craftbuzzwonky4752 3 ปีที่แล้ว

      You too saw the video!!
      I see, you are a man of "NO U" culture here!

  • @NPC-rq9tp
    @NPC-rq9tp 7 ปีที่แล้ว

    At 18:00 , why not just use trig substitution. I tried it using 3^(1/2)/2 tan theta. It worked out alright.

  • @Zhardamon
    @Zhardamon 7 ปีที่แล้ว +3

    pure beauty...!

  • @aryanjha1302
    @aryanjha1302 ปีที่แล้ว +2

    Easiest integral on TH-cam
    31 min yt video - "no i don't think i will"

  • @LightYagami-on5lm
    @LightYagami-on5lm 6 ปีที่แล้ว +71

    When title says easy and time says half an hour
    🤔🤔🤔🤔🤔🤔🤔😱

  • @Harothir
    @Harothir 7 ปีที่แล้ว +1

    This is just what I needed for my summer.

  • @TheKillerSock
    @TheKillerSock 7 ปีที่แล้ว +3

    yea dog imma need you to check by differentiation

  • @davidgillies620
    @davidgillies620 5 ปีที่แล้ว +1

    It's also expressible in terms of "the" hypergeometric function 2F1.

  • @ronnykazadi559
    @ronnykazadi559 6 ปีที่แล้ว +3

    Can you do integral of (xtanxdx) ?

  • @harry_page
    @harry_page 7 ปีที่แล้ว +1

    The exasperation at 25:00, "This is not the whole question!!" XD
    And again at 29:45 "We're almost done, oh my god!"

  • @LucBogaert
    @LucBogaert 7 ปีที่แล้ว +7

    Running a marathon is easy compared to solving this integral 🤓

  • @strider_1237
    @strider_1237 5 ปีที่แล้ว

    You're videos are awesome! Please keep posting :)

  • @Far_Gem
    @Far_Gem 7 ปีที่แล้ว +53

    It kinda bothers me that you write "tan^-1" instead of "arctan", it makes it seem like you could get tan^-(1/3) by multiplying it with tan^(2/3).

    • @MC-mx1mt
      @MC-mx1mt 7 ปีที่แล้ว +2

      Florian Bender if you mean 1/tan x, he would write it as cot x

    • @monzur1947
      @monzur1947 7 ปีที่แล้ว +14

      Florian Bender tan^-1 is a standard notation for arctan

    • @GrouchierThanThou
      @GrouchierThanThou 7 ปีที่แล้ว +29

      I agree. It's bad form IMO to both use tan^-1(x) for arctan(x) as well as the tan^q(x) for (tan(x))^q within a single exercise.

    • @angelmendez-rivera351
      @angelmendez-rivera351 7 ปีที่แล้ว +9

      Monzur Rahman We're aware, but it's a terrible notational standard.

    • @GrouchierThanThou
      @GrouchierThanThou 7 ปีที่แล้ว +2

      It's not even a "standard" notation really. Just a commonly used one (and not even as commonly used as the arctan notation).

  • @jihanhamdan5465
    @jihanhamdan5465 7 ปีที่แล้ว

    To solve for B and C in partial fraction decomposition do the same as u did for A but find for that expression a complex root, substitute then compare

  • @roceb5009
    @roceb5009 7 ปีที่แล้ว +3

    Okay so you've done sqrt tan x, you've done cube root tan x, can you generalize? Nth root tan x ?

  • @izzy31337
    @izzy31337 7 ปีที่แล้ว

    I love how you are so passionate about maths

  • @Bludgeoned2DEATH2
    @Bludgeoned2DEATH2 7 ปีที่แล้ว +3

    Dr. BalckPenRedPen, please check the answer by differentiation :)

  • @TheTimeDilater
    @TheTimeDilater 7 ปีที่แล้ว +1

    seems like a deep breathtaking moment when you got the answer to be this long...

  • @thewatcherinthecloud
    @thewatcherinthecloud 7 ปีที่แล้ว +5

    ...And when you want to take a break from listening to this video, you are going to SUBSTITUTE IT for one of the easier/more beautiful ones to understand :D Like sin(z)=2

  • @rohankodibagkar2552
    @rohankodibagkar2552 2 ปีที่แล้ว +1

    "and then we have to get back to the U world, and then we have to go back to the X world."
    What a wild ride - we're going on interplanetary journeys solving this integral!

  • @jousif650
    @jousif650 7 ปีที่แล้ว +13

    It is too long, not too hard. Anyway I doubt anyone can do it in any exam without making a small mistakes ☺

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +9

      it's like running a marathon (well, almost...)

  • @tomhimler8175
    @tomhimler8175 7 ปีที่แล้ว +2

    You know what you have to do now? Now you have to do the integral of (tanhx)^(1/3). These videos are the best please keep posting them!

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว

      Tom Himler Edward can help me with that. :)

    • @lezhilo772
      @lezhilo772 7 ปีที่แล้ว

      Just substitute the i's in the right places! tan(x) = -i tanh (ix), so you get tanh(x)=i tanh(-ix). Substitute this into the original integrand you get the cube root of i which is exp(i*pi/6), then you get an i outside when you replace dx with d(-ix). So the answer to integrating cube root of tanhx is just the original answer with all the x's replaced by -ix's, and an extra factor of exp(i*pi*2/3). Somehow you should be able to simplify everything in the end expression to show that the thing is real XD

  • @Centauri902
    @Centauri902 7 ปีที่แล้ว +5

    now the nth root

  • @nickriat7005
    @nickriat7005 7 ปีที่แล้ว +1

    If every question on the test is like this Mr. Chow, I might have to clear my whole weekend to complete it.

  • @robertherbert8419
    @robertherbert8419 7 ปีที่แล้ว +5

    ....It wasn't that bad....it didn't have limits to substitute (hehe ! )

  • @DougCube
    @DougCube 7 ปีที่แล้ว

    Integrand has a period of pi. It's real-valued from [0,pi/2) and complex-valued from (pi/2,pi). Goes to +inf at pi/2.

  • @harshag.2085
    @harshag.2085 7 ปีที่แล้ว +6

    To be fair, I have dealt with much tougher problems. Even on TH-cam.

    • @blackpenredpen
      @blackpenredpen  7 ปีที่แล้ว +20

      share, yea?

    • @raimonwintzer
      @raimonwintzer 7 ปีที่แล้ว +11

      *smashes bottle on counter, holding its jagged remains menacingly* yea?

    • @dynamic-eu1794
      @dynamic-eu1794 7 ปีที่แล้ว +6

      Wow you so smart you must watch Rick and Morty

    • @harshag.2085
      @harshag.2085 7 ปีที่แล้ว

      Rick and Morty is a fun show, nothing to do with being smart lol

    • @harshag.2085
      @harshag.2085 7 ปีที่แล้ว +2

      I didn't mean to say this is an easiest integral lol. It is a tough problem, but not the hardest I meant to say

  • @nope110
    @nope110 4 ปีที่แล้ว +1

    I think its so strange that this integral is so tough, but i could solve it myself, like i understood every step, i knew what to do to get there myself, it just takes so many steps. Thats the first time ive been able to say that about a tough maths problem on youtube, its a good feeling.

    • @maalikserebryakov
      @maalikserebryakov 2 ปีที่แล้ว

      dude same 😭
      To think i can finally keep up with some videos on this channel

  • @v_saaam
    @v_saaam 7 ปีที่แล้ว +3

    Everytime he says 'something' I hear 'sensei' *_*

    • @JorgetePanete
      @JorgetePanete 7 ปีที่แล้ว +1

      Samarth Varshney or... passdee instead of positive. Forgive him, neither him or me are english ppl

  • @angelogandolfo4174
    @angelogandolfo4174 3 ปีที่แล้ว

    That was a really enjoyable lil’ video. Thank you, it was a nice little refresher! 🙂