I couldn't do this integral when I was 3...

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  • Опубліковано 3 гру 2019
  • We will integrate ln(1-e^x) with a special math function called the polylogarithm function.
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КОМЕНТАРІ • 420

  • @blackpenredpen
    @blackpenredpen  4 роки тому +450

    Like the purple thumbnail?

    • @VisharadSrivastava
      @VisharadSrivastava 4 роки тому +8

      blackpenredpen Yeah

    • @subhadipbardhan9711
      @subhadipbardhan9711 4 роки тому +8

      Yup

    • @alexdemoura9972
      @alexdemoura9972 4 роки тому +7

      Purple pen, yes, but please no blue faces on me, no drama, when I was 3, I could barely speak and walk. Best I could do with multiple colors crayon box was eating some of crayons and getting into a big trouble after manifesting my art on the walls of my parents' home.
      No Intergrals, no Internet, no UA-cam, no blackpenredpen...

    • @user-yk2rc4us5u
      @user-yk2rc4us5u 4 роки тому

      네 좋아요

    • @MathIguess
      @MathIguess 4 роки тому +2

      It's nice :)

  • @momozuke2757
    @momozuke2757 4 роки тому +768

    The chemist in me is very impressed you created lithium from this integral.

    • @yogitshankar6348
      @yogitshankar6348 4 роки тому +3

      lol

    • @Metalhammer1993
      @Metalhammer1993 4 роки тому +77

      Hope he doesn't clean the white board with water xD

    • @jagatiello6900
      @jagatiello6900 4 роки тому +19

      It won't last long anyway because of Li-5 half life...by the time he completed the expression it became pure helium already, haha

    • @dlevi67
      @dlevi67 4 роки тому +9

      Surely, since s = 2 it's dilithium?

    • @cansabanci
      @cansabanci 4 роки тому +3

      @@dlevi67 no, Lithium doesn't work like that

  • @tanelkagan
    @tanelkagan 4 роки тому +415

    Don't feel bad, I couldn't do this integral when I was 3 either.

    • @blackpenredpen
      @blackpenredpen  4 роки тому +105

      Glad to hear that I am no alone.

    • @leonhardeuler6811
      @leonhardeuler6811 4 роки тому +8

      @@blackpenredpen Wait I'm kinda dumb, are we being sarcastic here or did you actually learn calculus at 3?

    • @christianalbertjahns2577
      @christianalbertjahns2577 4 роки тому +17

      @@leonhardeuler6811 you did learn calculus at 3 years old, right?

    • @leonhardeuler6811
      @leonhardeuler6811 4 роки тому +3

      @@christianalbertjahns2577 no, I learned calculus at 12. Now I feel kinda dumb...

    • @christianalbertjahns2577
      @christianalbertjahns2577 4 роки тому +10

      @@leonhardeuler6811 serious question. did the real Euler learn calculus at 12? I honestly don't know

  • @px64
    @px64 4 роки тому +239

    When I was three, I didn't even knew the
    6D (2,0)-superconformal field theory which has no Lagrangian description, is holographically dual to M-theory on AdS7 x S", and when compactified on St gives 5D maximally supersymmetric Yang-Mills

    • @antonquirgst2812
      @antonquirgst2812 4 роки тому +36

      exactely - bothered the crap out of me until I got 6... tough times... tough times!

    • @createyourownfuture5410
      @createyourownfuture5410 2 роки тому +7

      You still don't know that verbs are used as infinitives when paired with do/does/did/(neg)!

    • @rkchoka101
      @rkchoka101 2 роки тому +1

      That’s basic dude

    • @QuantenMagier
      @QuantenMagier 2 роки тому +1

      But is it also conformant to the five-dimensional Kaluza-Klein theory? Otherwise I would not trust it, and rather take a lolly from a stranger..

    • @bruhe8895
      @bruhe8895 5 місяців тому +1

      wtf... I knew that the second I was born

  • @OonHan
    @OonHan 4 роки тому +45

    when i was 3 i didn't know how to integrate sqrt(tan x) but now...
    i still dont know

    • @blackpenredpen
      @blackpenredpen  4 роки тому +11

      You can do it!

    • @OonHan
      @OonHan 4 роки тому +3

      blackpenredpen thanks!!!

    • @mr.tommy__8586
      @mr.tommy__8586 2 роки тому +1

      @@blackpenredpen oh man I can't understand that solution

  • @gabrielthompson9800
    @gabrielthompson9800 4 роки тому +182

    When I was 3 I still didn't fully understand the Fourier transform

    • @lopkobor6916
      @lopkobor6916 4 роки тому +12

      The Bloody Doctor This is so sad. Alexa, play Despacito.

    • @ramone.chacon5084
      @ramone.chacon5084 4 роки тому +7

      nah thats nothing, when i was 4 i had problems to understand the fundamental theorem of calculus :''v

    • @colinjava8447
      @colinjava8447 2 роки тому +2

      When I was 6 months old I couldn't prove the Riemann Hypothesis.

    • @DendrocnideMoroides
      @DendrocnideMoroides Рік тому

      you did not fully understand it but partially understanding is also good at 3

  • @juansamudio1171
    @juansamudio1171 4 роки тому +27

    When I was 3 I wasn’t able to prove the poincare conjecture but now

  • @jegasi8082
    @jegasi8082 4 роки тому +31

    Him when he was 3: who are you?
    Him now: I'm you but smarter

    • @Kitulous
      @Kitulous 4 роки тому

      nevertheless he at 3 was smarter than me rn

  • @terrencelau5207
    @terrencelau5207 4 роки тому +75

    When I was 3 I tried to solve 1+1

    • @crismal6477
      @crismal6477 4 роки тому

      Terrence Lau when I was 3 I was only able to do 1+2 then now I’m 10 years older and I can do derivatives but integrals are kind of hard but I can still do some

    • @hipepleful
      @hipepleful 4 роки тому

      Well, what's the answer?

    • @terrencelau5207
      @terrencelau5207 4 роки тому

      @@hipepleful I think is 6

    • @hipepleful
      @hipepleful 4 роки тому

      @@terrencelau5207 hm... Sounds about right. Maybe it's 11? idk.

    • @terrencelau5207
      @terrencelau5207 4 роки тому

      @@hipepleful big brain

  • @maskedman8368
    @maskedman8368 4 роки тому +5

    this mans work always relaxes me , he makes things smooth, true troubleshooter in math

  • @kevinbaudin9557
    @kevinbaudin9557 4 роки тому +69

    When you were e years old, I'm sure you could have done it. For a fraction a time.

    • @Thaplayer1209
      @Thaplayer1209 4 роки тому +3

      Kevin Baudin e is not rational

    • @kevinbaudin9557
      @kevinbaudin9557 4 роки тому +4

      @@Thaplayer1209 I was sure someone would jump on me about that "fraction of time" :P

  • @bjorncedervall5291
    @bjorncedervall5291 3 роки тому +21

    I was into practical physics at age two - put a nail into an electric outlet. Was later pretty good at math but now, being retired, I still couldn't do this integral without help - essentially however, confused by the lithium.

  • @electrovector7212
    @electrovector7212 4 роки тому +3

    When I was 3 I couldn't speak lol

  • @sleeper6091
    @sleeper6091 4 роки тому +10

    I was eating sand and licking wet paint when I was three years old.

  • @atomics.h.1824
    @atomics.h.1824 4 роки тому +5

    When i was 3, I wasn't even born.

  • @harshitbamotra2013
    @harshitbamotra2013 4 роки тому +2

    When I was 3, I used to piss my pants.

  • @shambosaha9727
    @shambosaha9727 4 роки тому +12

    Me: Perfect squares are great
    Also me: *Sees 289 comments, decides to ruin it.

  • @mokouf3
    @mokouf3 3 роки тому +1

    When I was 3 years old, the mathematician (Euler?) inventing e and ln was not born yet.

  • @donlansdonlans3363
    @donlansdonlans3363 4 роки тому +11

    The subtitles say "when I was jesus" ahaha

  • @sergioh5515
    @sergioh5515 4 роки тому +3

    Wow super cool :3 you're always posting the best stuff 😅

  • @shotto9167
    @shotto9167 3 роки тому +1

    I don't know what I was doing when I was 3 years old, I guess I was speaking with my imaginary friends.

  • @maliciousmarka
    @maliciousmarka 4 роки тому

    Great Christmas video!

  • @NeonArtzMotionDesigns
    @NeonArtzMotionDesigns 4 роки тому +1

    When I was 3, I began my proof of the Riemann hypothesis which requires for one to integrate this

  • @VibingMath
    @VibingMath 4 роки тому +9

    Great man! There are 3 amazing things in this video. The polylogarithm and zeta functions, and 3B1B as your patreon! 😁😁

  • @JensenPlaysMC
    @JensenPlaysMC 4 роки тому +4

    about 6 months ago i studied A level maths (in uk which is studied at college) and i got an A* and i couldnt have done it without u. you helped me pretty much learn everything in the calculus part of the specification before my teacher even started to teach the calculus part ! thanks for your videos

  • @VincentKun
    @VincentKun 4 роки тому +1

    You're truly an *Entertainer*

  • @MrLeobergonci
    @MrLeobergonci 4 роки тому

    Do more videos about polylogarithm, please!

  • @ralfbodemann1542
    @ralfbodemann1542 4 роки тому +8

    When I was three, I faced a lot of discussions among my multiple personalities.
    Anyway: Thanks for the nice birthday present!

    • @MathswithMuneer
      @MathswithMuneer 4 роки тому

      Ralf Bodemann see mine videos on mathematics, may be you have more gifts.

    • @chrisfer2733
      @chrisfer2733 4 роки тому

      Happy birthday buddy!

  • @angelmendez-rivera351
    @angelmendez-rivera351 4 роки тому +17

    It may have been better to also introduce the integral definition of the polylogarithms and how it relates to the Taylor series expansion.

  • @hamsterdam1942
    @hamsterdam1942 4 роки тому +2

    I can do it faster
    integral of ln(1-e^x)dx= ℵ(x) + C, where ℵ(x) - some special alef function

  • @shoobadoo123
    @shoobadoo123 4 роки тому

    I cried more here than at my grandma’s funeral...

  • @sharmashish9
    @sharmashish9 4 роки тому +5

    I m Physics student but love to watch your channel it's very useful for physics student too lots respect from india 🙏🏼🙏🏼🙏🏼

    • @MathswithMuneer
      @MathswithMuneer 4 роки тому +1

      Ashish Sharma good one. Check the way I am teaching it.

  • @jamesbentonticer4706
    @jamesbentonticer4706 3 роки тому

    When I was 3 years old I had almost gained full control of my neck.

  • @ianmoseley9910
    @ianmoseley9910 4 роки тому

    I was about 7 when I started solving simple algebra problems in my father's old school books. Did not really understand what it was all about but got right answers to the basic questions.

  • @mohammadcheshomi4261
    @mohammadcheshomi4261 2 роки тому

    It was great. Thank you

  • @xevira
    @xevira 4 роки тому +2

    One of these days, BPRP will do something so complicated on the board, he will have to rename his channel to rainbowpen because of the sheer number of colors he had to use. :D

  • @mohammedsrivastava5917
    @mohammedsrivastava5917 4 роки тому

    I literally tried 1 hour...! Very brilliant solution..!

  • @19TonsOfGold
    @19TonsOfGold 2 роки тому

    When I was 3 I couldn't even derive e^x

  • @MrQwefty
    @MrQwefty 4 роки тому +1

    Hey BPRP, I'm having trouble in Calc 1 with limits and whatnot. I understand almost every single theorem, test and identity individually, when the teacher shows them on the board, but when it comes to figuring out which of them to choose when solving a specific question, I find myself fumbling, using one method and only 10 lines later realizing I should be using a different method.
    Do you have any recommendations for how to know in advance what method to use to solve a question just by looking at it?
    Thank you for all the amazing videos!! :D

  • @MathIguess
    @MathIguess 4 роки тому +1

    Lu Chen :O that's great!

  • @alexandergarcia6479
    @alexandergarcia6479 4 роки тому

    please make more videos about summations

  • @heartroschach
    @heartroschach 4 роки тому

    When I was 3, I can't even talk.

  • @abhishektiwari7385
    @abhishektiwari7385 4 роки тому

    The integration is done somewhat in restrictive condition |u| |e^x| ln(e^(x)(e^(-x)-1)). Now e^(-x)

  • @neilgerace355
    @neilgerace355 4 роки тому +6

    7:00 wondering when you were going to get back to the x world :)

  • @bhavydugar6665
    @bhavydugar6665 2 роки тому +2

    Hey even I couldn’t do it when I was 3 boy we have so much in common

  • @chaoticoli09
    @chaoticoli09 4 роки тому

    @Blackpenredpen Next, compute the integral where the original integrand is squared! I wonder how the answer changes

  • @CengTolga
    @CengTolga 3 роки тому +3

    If 1/(1-u) = Σ(...) only works for |u|

  • @cedric1731
    @cedric1731 4 роки тому +2

    The thing is that I believe you when you say you tried with 3 years...

  • @harshvardhanraghav95383
    @harshvardhanraghav95383 3 роки тому +2

    Dear sir ,Can we make it a definite integral

  • @anonymousaccount8234
    @anonymousaccount8234 4 роки тому

    I rewatched some moments for few times but when i understood it i was like: "WOOOOOOAOAOAOO"
    Brilliant, thank you.

  • @neilgerace355
    @neilgerace355 4 роки тому +3

    The music is Scott Joplin's The Entertainer

  • @6099x
    @6099x 4 роки тому +1

    "I know christmas is coming, but lets go to the u-World anyway " hahaha Okay lets go!

  • @lunam7249
    @lunam7249 3 роки тому

    I couldn’t walk on water when I was 3....but by 4 I was running on water!!!!

  • @wecreatealways
    @wecreatealways 4 роки тому +1

    When I was 3, I didn't have best friend to help me.

  • @starsun7455
    @starsun7455 2 роки тому

    Great lecture. But it is so sad |u| is limited

  • @ElPastalero
    @ElPastalero 4 роки тому

    You could say a lot of applicable things with "when i was 3 i couldn't ___"

  • @mike4ty4
    @mike4ty4 4 роки тому +3

    Great. Now that you have PolyLog, you can integrate tan(sqrt(x)) and tan(cbrt(x)) - the natural "complements" to favorite problems featured here.

  • @matthewfuerst6456
    @matthewfuerst6456 4 роки тому +1

    When you take the log of something, an exponentiation turns into a multiplication. A multiplication turns into an addition. Can addition split into something else?

  • @Theraot
    @Theraot 4 роки тому +1

    Use the chen lu clip playing backwards

  • @StarOfAthenry
    @StarOfAthenry 4 роки тому +1

    Could you explain how you went from line 3 to line 4 (left hand side)? How is that you simplified the 1/u term?

    • @darkseid856
      @darkseid856 4 роки тому

      We have u^n /u . We can write it as u^(n-1) .
      It's a simple property we learned in school . (a^m) ÷ (a^n) = a^(m-n)

  • @ginsburgchannel3695
    @ginsburgchannel3695 2 роки тому

    3:55 still have no idea for over years this part ; you were multipling the u^n-1 with an u to get u^n , so why the denominator you multiplied it only with n ?

  • @JSSTyger
    @JSSTyger 4 роки тому

    My first grade teacher put me in detention for solving this problem.

  • @bipolarbanana997
    @bipolarbanana997 4 роки тому +7

    WTF. You knew how to do integrals at 3? Im 14 and in Algebra 2 but have no idea what an integral even is

  • @chocoice9
    @chocoice9 4 роки тому +1

    Same man... Same....

  • @Peter_1986
    @Peter_1986 2 роки тому +1

    I couldn't do this integral when I was 3 years old either.

  • @dzakytamir3048
    @dzakytamir3048 4 роки тому +1

    When I saw in Wolfram alpha, I haven't knew the Li means. After I saw this video, now I know what's that mean,, Thanks Blackpenredpen

  • @Ocklepod
    @Ocklepod 2 роки тому

    feels so bad that the polyLOG doesn't cancel with e^x

  • @walterengler5709
    @walterengler5709 4 роки тому

    This was so easy to do what I was three. First I took the blue crayon and added ears, then the green to add grass, then I chewed on the red crayon and clapped a bit all done!

  • @easygoing1719
    @easygoing1719 4 роки тому

    Well you were probably not able to integrate Christmas into the Integral properly...

  • @fried_ady6318
    @fried_ady6318 9 місяців тому

    How did you produce the sum?

  • @nuklearboysymbiote
    @nuklearboysymbiote 4 роки тому

    From now on I shall refer to substitution as ”Lu Chen”

  • @MathIguess
    @MathIguess 4 роки тому +9

    8:02 that brief rap xD nice!

  • @darkslayer9936
    @darkslayer9936 4 роки тому +1

    Wait I couldn't able to do this even when I was 13

  • @zeraiwissem4715
    @zeraiwissem4715 4 роки тому +3

    When I was 3 years old I didn't know even my age XD

  • @hakkbak
    @hakkbak 4 роки тому +1

    Why can't you use the substitution u = (1 - e^x) for the integral
    Wouldn't that give (u-1)ln(u) which can be split into two fairly straightforward integrals?

  • @Jhev1000
    @Jhev1000 4 роки тому +1

    Hahaha, love the title!

  • @Anik_Sine
    @Anik_Sine 2 роки тому

    When I was 6 I asked why planets don't fall down

  • @shuidongliu954
    @shuidongliu954 4 роки тому +2

    Could you rewrite it as 1 * ln(1-e^x) then use the same substitution and just solve with integration by parts?

    • @angelmendez-rivera351
      @angelmendez-rivera351 4 роки тому

      Lewis Clarke Not at all. This integral is non-elementary. You cannot do anything to it to evaluate to any non-special function. No Feynman integration, no integration by parts, no u-sub, no trig identities, no nothing. You *can't do it with elementary functions.* Do you understand this?

  • @Cat-yz1tk
    @Cat-yz1tk 4 роки тому +3

    Is it connected to the logarithmic integral function?

  • @Patapom3
    @Patapom3 4 роки тому

    Amazing!

  • @thedoublehelix5661
    @thedoublehelix5661 4 роки тому

    Interchange of limits!

  • @urironen250
    @urironen250 4 роки тому +3

    How can you use the series for ln(1-u) if clearly there are some u that are bigger than one?

    • @arnav257
      @arnav257 4 роки тому

      There can't be any. Not in the real world.

    • @urironen250
      @urironen250 4 роки тому

      @@arnav257 what is the absolute value of 100?

    • @arnav257
      @arnav257 4 роки тому +1

      @@urironen250 The natural logarithmic function restricts its domain to positive numbers. For all u>1, ln(1-u) is not real. I don't see what your absolute value comment was even about. e^x is bounded by 0 and 1 here. Period.

    • @darkseid856
      @darkseid856 4 роки тому +1

      Yes there are . But the point is you can't possibly use a value of u bigger than one . Because logarithmic function do not accept -ve values . (in real world)

    • @arnav257
      @arnav257 4 роки тому

      @@darkseid856 Thereby restricting the values of u. What was the point of this futile exercise in reasoning?

  • @hiler844
    @hiler844 4 роки тому

    when he was 3 ... hundred years old

  • @gregoriousmaths266
    @gregoriousmaths266 4 роки тому +4

    when i was 3, 3^2=-1

  • @holyshit922
    @holyshit922 4 роки тому

    Calculating by parts we will get integral of exponential generating function of Bernoulli numbers

  • @thomasblackwell9507
    @thomasblackwell9507 4 роки тому

    THE COLORS!! THE COLORS!!

  • @Metalhammer1993
    @Metalhammer1993 4 роки тому

    stupid question, as the best friend only works for IuI

  • @nicholasjuricic3683
    @nicholasjuricic3683 2 роки тому

    I couldn't do it at 10. Still not at 11. What a life.

  • @pseudoexpertise7739
    @pseudoexpertise7739 Рік тому

    What it u is greater than or equal to one? Or speaking of the x world, for e^x, if x is greater than or equal to zero?

  • @liftNtricks
    @liftNtricks Рік тому

    isnt id doable using simply part integration?

  • @ananyapathak8701
    @ananyapathak8701 4 роки тому +1

    Now he must be π^e or e^π yrs old.

  • @vishalk2802
    @vishalk2802 4 роки тому

    I dont know about polylogarithms ,can you share the video explaining them

  • @googleuser4063
    @googleuser4063 4 роки тому +1

    When I was 3 , I thought that I could do this question when I will be ln(0) years old. Lol

  • @StuartSimon
    @StuartSimon 2 роки тому +1

    In what place does anybody do integrals when they are three years old?

  • @thomaskim5394
    @thomaskim5394 4 роки тому

    To use the summation of u^n, the absolute value of u is less than 1. But when you take the integral, there is no restriction on u. So, the solution is wrong?

  • @212ntruesdale
    @212ntruesdale 4 роки тому

    At 2:08, you add a constant for having just integrated. C will = 0 provided that -ln(1-u)=the infinite sum, which it does when u=0. So fine to not write +C by choosing u=0. Except that u=e^x, which does not = 0 for all reals. Can you please explain? Thanks.

    • @elilogan8630
      @elilogan8630 2 роки тому

      if you know f(x)=2x+c, plugging in a value for x and comparing to known values of f(x) will allow you to determine c

  • @DragasGaming
    @DragasGaming 4 роки тому +1

    Is this true only for when |exp(x)| < 1 then?

  • @ianmoseley9910
    @ianmoseley9910 4 роки тому

    Poly logarithm - nice girl, friend of Napier

  • @jayakhandelwal3900
    @jayakhandelwal3900 4 роки тому

    This integral should be named as the lithium integral

  • @vukstojiljkovic7181
    @vukstojiljkovic7181 4 роки тому

    We could have done it by making ln(1-x) into a summation, but a nice way to do it in your way too :)