The Easiest Integral on YouTube

Yes, I am serious.
blackpenredpen

[wellbangok]

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

[BTM]

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

[friendofjim]

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

[yoavcarmel]

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

[rileywells]

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!

[flansterr]

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

[tipoima]

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

[natalieeuley]

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! 🤓🤓🤓

[davidkippy]

You're going from blackpenredpen to 3blue1brown

[andresvivas]

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 Would you check the answer by diferentiation???? Please :)

[shakirahsanromeo]

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

[bonbonpony]

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

[maxhaibara]

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

[JoJoJet]

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

[azmath]

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.

[sethleverett]

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

[particleonazock]

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

[malayagr]

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:

[ianbo]

Worth every second of the watch. Thank you!

[ATeamBrown]

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