I couldn't do this integral when I was 3...
Вставка
- Опубліковано 3 гру 2019
- We will integrate ln(1-e^x) with a special math function called the polylogarithm function.
Subscribe for more math for fun videos 👉 bit.ly/3o2fMNo
💪 Support this channel, / blackpenredpen
🛍 Shop math t-shirt & hoodies: bit.ly/bprpmerch. (10% off with the code "WELCOME10")
🛍 I use these markers: amzn.to/3skwj1E
Like the purple thumbnail?
blackpenredpen Yeah
Yup
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...
네 좋아요
It's nice :)
The chemist in me is very impressed you created lithium from this integral.
lol
Hope he doesn't clean the white board with water xD
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
Surely, since s = 2 it's dilithium?
@@dlevi67 no, Lithium doesn't work like that
Don't feel bad, I couldn't do this integral when I was 3 either.
Glad to hear that I am no alone.
@@blackpenredpen Wait I'm kinda dumb, are we being sarcastic here or did you actually learn calculus at 3?
@@leonhardeuler6811 you did learn calculus at 3 years old, right?
@@christianalbertjahns2577 no, I learned calculus at 12. Now I feel kinda dumb...
@@leonhardeuler6811 serious question. did the real Euler learn calculus at 12? I honestly don't know
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
exactely - bothered the crap out of me until I got 6... tough times... tough times!
You still don't know that verbs are used as infinitives when paired with do/does/did/(neg)!
That’s basic dude
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..
wtf... I knew that the second I was born
when i was 3 i didn't know how to integrate sqrt(tan x) but now...
i still dont know
You can do it!
blackpenredpen thanks!!!
@@blackpenredpen oh man I can't understand that solution
When I was 3 I still didn't fully understand the Fourier transform
The Bloody Doctor This is so sad. Alexa, play Despacito.
nah thats nothing, when i was 4 i had problems to understand the fundamental theorem of calculus :''v
When I was 6 months old I couldn't prove the Riemann Hypothesis.
you did not fully understand it but partially understanding is also good at 3
When I was 3 I wasn’t able to prove the poincare conjecture but now
When I was 3 I tried to solve 1+1
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
Well, what's the answer?
@@hipepleful I think is 6
@@terrencelau5207 hm... Sounds about right. Maybe it's 11? idk.
@@hipepleful big brain
Him when he was 3: who are you?
Him now: I'm you but smarter
nevertheless he at 3 was smarter than me rn
this mans work always relaxes me , he makes things smooth, true troubleshooter in math
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.
I was eating sand and licking wet paint when I was three years old.
When you were e years old, I'm sure you could have done it. For a fraction a time.
Kevin Baudin e is not rational
@@Thaplayer1209 I was sure someone would jump on me about that "fraction of time" :P
When I was 3 I couldn't speak lol
Me: Perfect squares are great
Also me: *Sees 289 comments, decides to ruin it.
When I was 3, I used to piss my pants.
When i was 3, I wasn't even born.
I can do it faster
integral of ln(1-e^x)dx= ℵ(x) + C, where ℵ(x) - some special alef function
The subtitles say "when I was jesus" ahaha
Wow super cool :3 you're always posting the best stuff 😅
Thanks!
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.
Ian moseley good
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
same
Do more videos about polylogarithm, please!
When I was 3 years old, the mathematician (Euler?) inventing e and ln was not born yet.
Great man! There are 3 amazing things in this video. The polylogarithm and zeta functions, and 3B1B as your patreon! 😁😁
Mak Vinci yea thank you!!!
Great Christmas video!
You're truly an *Entertainer*
When I was three, I faced a lot of discussions among my multiple personalities.
Anyway: Thanks for the nice birthday present!
Ralf Bodemann see mine videos on mathematics, may be you have more gifts.
Happy birthday buddy!
When I was 3, I began my proof of the Riemann hypothesis which requires for one to integrate this
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
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?
please make more videos about summations
If 1/(1-u) = Σ(...) only works for |u|
I don't know what I was doing when I was 3 years old, I guess I was speaking with my imaginary friends.
The integration is done somewhat in restrictive condition |u| |e^x| ln(e^(x)(e^(-x)-1)). Now e^(-x)
@Blackpenredpen Next, compute the integral where the original integrand is squared! I wonder how the answer changes
The music is Scott Joplin's The Entertainer
It may have been better to also introduce the integral definition of the polylogarithms and how it relates to the Taylor series expansion.
I m Physics student but love to watch your channel it's very useful for physics student too lots respect from india 🙏🏼🙏🏼🙏🏼
Ashish Sharma good one. Check the way I am teaching it.
I cried more here than at my grandma’s funeral...
I literally tried 1 hour...! Very brilliant solution..!
I rewatched some moments for few times but when i understood it i was like: "WOOOOOOAOAOAOO"
Brilliant, thank you.
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 ?
It was great. Thank you
How did you produce the sum?
Dear sir ,Can we make it a definite integral
Hey even I couldn’t do it when I was 3 boy we have so much in common
Calculating by parts we will get integral of exponential generating function of Bernoulli numbers
Great lecture. But it is so sad |u| is limited
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?
Lu Chen :O that's great!
Could you explain how you went from line 3 to line 4 (left hand side)? How is that you simplified the 1/u term?
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)
Is this true only for when |exp(x)| < 1 then?
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
7:00 wondering when you were going to get back to the x world :)
Great. Now that you have PolyLog, you can integrate tan(sqrt(x)) and tan(cbrt(x)) - the natural "complements" to favorite problems featured here.
When I was 3 years old I had almost gained full control of my neck.
The thing is that I believe you when you say you tried with 3 years...
"I know christmas is coming, but lets go to the u-World anyway " hahaha Okay lets go!
stupid question, as the best friend only works for IuI
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
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?
Nope, you get ln(u)/(u-1)
Turn on captions
Could you rewrite it as 1 * ln(1-e^x) then use the same substitution and just solve with integration by parts?
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?
We could have done it by making ln(1-x) into a summation, but a nice way to do it in your way too :)
when i was 3, 3^2=-1
Lol how?
Because i=sqrt(-1)
You may laugh now
isnt id doable using simply part integration?
Same man... Same....
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?
Shouldn't it be divided by u as the numerator is getting multiplied by u??
Find the sum of all possible integers for K so that the equation 3x^4 - 3x^2 + 2x -k = 0 has an odd number of real roots in the range ]-2.1[.
When I was 3 I couldn't even derive e^x
I got the same expression as the integrand wtf
I used by parts method.. taking 1 as second part and the original term as first.
How can you use the series for ln(1-u) if clearly there are some u that are bigger than one?
There can't be any. Not in the real world.
@@arnav257 what is the absolute value of 100?
@@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.
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)
@@darkseid856 Thereby restricting the values of u. What was the point of this futile exercise in reasoning?
Um dia vou poder entender o que você fala, mas só em ver já aprendo algumas coisas. Você é bom cara. Obrigado.
In(1-e^x)= ln1-ln e^x isn't that law of distribution
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.
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
Is it connected to the logarithmic integral function?
GGEZL Not really
Use the chen lu clip playing backwards
In what place does anybody do integrals when they are three years old?
As a living human person, I am surprised to see how Lithium can connect with such complex Calculus topics.
WTF. You knew how to do integrals at 3? Im 14 and in Algebra 2 but have no idea what an integral even is
r/wooosh
Sai Panda r/ihavereddit
8:02 that brief rap xD nice!
Werner Steyn hahahahaha nice thanks!!!
Nice beat to go with it too!
I dont know about polylogarithms ,can you share the video explaining them
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!
I couldn’t walk on water when I was 3....but by 4 I was running on water!!!!
I couldn't do this integral when I was 3 years old either.
When I was 3, I can't even talk.
When I was 3, I didn't have best friend to help me.
Interchange of limits!
If this is li, how do I write logarithmic integral
Keep in mind that the title doesnt necessarily mean that he could do other integrals at that age.
Can’t you do it with out series? Make u-sub then integrate by parts I think it will work.
No doesn’t only with series
You could say a lot of applicable things with "when i was 3 i couldn't ___"
Can somebody explain how at 3:48 he gets u^n/n² from u^(n-1)/n ?
THE COLORS!! THE COLORS!!
When I was 3 years old I didn't know even my age XD
Amazing!
Can u integral of sqrt(2+cos^3x)dx
neither did i . my first contact with infinitesimal calculus happened when i was 12 and wondered what all these strange notations stand for.