The Easiest Integral on YouTube
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- เผยแพร่เมื่อ 13 ส.ค. 2017
- He did the derivative!!! Check out Fematika • Checking BlackPenRedPe...
100 integrals: • 100 integrals (world r...
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Yes, I am serious.
blackpenredpen
OK, I checked the answer and it was correct! th-cam.com/video/mUXdgY5MeEg/w-d-xo.html
Happy New Year!!!
I approve.
Lol, just finished the vid and relaised this
Oh god my maths test is on 1st Aug and I haven't prepared for it yet...... integrals is also in test!😢😢😢
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.
i really need your help to intigrate this for me i really need it ----- x-1*sqrt.2x-x*2
/x+1
You know it's a hard problem when he has to use 3 colors
BT7M yup
blackpenredpenbluepen
This is not hard prblm we indians take 30 sec to solve this
@@g.peloni3694 none cause we never and then we're like wtf are we doing.
@@g.peloni3694 uff...😂I'm also An Indian I'm a Calculus Lover too...
Somewhere out there, a professor is gonna watch this video and make this problem a test question. RIP.
Sheev Palpatine Saw the comment, liked for the name
Sheev Palpatine I just had to pin this comment.
oh no, don't give them ideas
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
Sheev Palpatine did you ever hear the tragedy of darth plagueis the wise?
Check the answer by differentiation
You mad man
You'll break him
I didn't understand the joke until I saw the answer XD
Avi Mehra The mad lad actually did it
Integrate it again.
I don't want you to check your answer by differentiation. I want you to integrate your answer :D
BRUH
xD
You're a monster
That’s easy
@@asparkdeity8717 yeah ok
8:15 *erases that additional line*
ohh god thank youu
yoav carmel lollllll nice catch!!!!
Android Ninja yup
Wow
I think you did a step wrong somewhere, please differentiate it to check.
Lolololol
You're going from blackpenredpen to 3blue1brown
How so? His vids are way cooler
Because this is really REALLY complicated yet you manage to explain it so well. Its cool at the same time
blackpenredpen Because of the color markers you are using
blackpenredpen and sometimes blue : )
blackpenredpenbluepengreenpen
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 :)
lol! I am waiting for some viewers to do it!
blackpenredpen We want you to check it by differentiation. It's always easier than the integration, right?
blackpenredpen I proved it using my calculator. Is that good enough?
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! ....)
Maybe?!
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!
Riley Wells my pleasure!!!!
@@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.
I have a challenge for you. Make the generalization of the integral of n-th root of tan x dx
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.
of course, I'm ignoring any possible trig manipulations ...
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.)
Kyro well Oh yeah..
Lol that's sadistic!
I fear you may run out of substitute variables one day :P
Shakir Ahsan Romeo probably. Next I will use alpha, beta
*creates new alphabet after using all latin, greek, cyrillic, hebrew and arabic letters*
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
After that start using ♤♡◇♧¤▪☆
How about हिन्दी
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! 🤓🤓🤓
Natalie Euley thank you Natalie!
30:40 "Please, do not ask me to check the answer by differentiation"
Hey, you should totally check the answer by differentiation!
He did the derivative!!!!!!!!!!!! Check out Fematika's
th-cam.com/video/as1vk0IuAHA/w-d-xo.html
Doctor: You have 31 minutes and eight seconds to live.
Me: immediately opens this video
Ok to the one dislike on the video I want you to post a follow up showing everyone how you do this integral.
Mace Jr there is no dislike now
NestorV S Hhh he couldn't do it.
Nah two people did.
disliking =/= "i can do better"
ask any sports fan if you don't believe me.
Now 5³ dislikes
Now do the integral of (tanx+(tanx)^(1/2)+(tanx)^(1/3)+(tanx)^(1/4)+(tanx)^(1/5)...)
Mr. Gentlezombie spoiler alert
this series will diverge, this question doesn't make sense.
@@aneeshsrinivas9088 D'oh!
Can you check the answer by differentiation ?
Pedro Bessa maybe one day :)
Really quick way to check. Takes 30 seconds. Plug in some values the the limit of integration and use fund. Thm of calc p2.
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
Ah!!! I like the pt u made at 18:18... and what u said "The dream is collapsing"
Worth every second of the watch. Thank you!
200%productions thank you!!
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.
Could you check the answer by differentiation?
no
yes
Maybe
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...
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!
Fetus?
Bro really spelled it with an o 💀
@@JMZReview diarrhoea
30:40 differentiASIAN
Lmao
Imagine doing a test and solving this problem. You did every step right, but you forgot to write plus C
And professor deducts 1mark for that
@@delta2884 my professor would tear the whole thing and give you 0 ;)
Easier when in France they ask for a antiderivative so you don't have to add +C
Calc II + Calc II
what about the tan(x) root of tan(x)?
I think impossible
NestorV S I thought you could integrate anything you wanted
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.
Ace Eternus
Some functions have no elementary anti derivative take x^x for example, you have to settle for a series.
Gregory House Tecnically there is a solution, but it just can't be expressed in terms of exponentials, polynomials, logarithms etc
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
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).
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.
I love how enthusiastic you are! What great videos you make.
Fantastic job of explaining every step!
Please differentiate this to get back to cuberoot of tan x
you are such an amazing teacher you make this advanced stuff seem so easy
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*🥳🥳
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
Thank you so much. I am very happy to hear your nice comment! Keep up the good work too!
I'm worried for you.
MistaTwoJeffreyTwenty Yaay
U should worry about my students
blackpenredpen oh noooo, show them sympathy please, they don't deserve this!
Lol! I am teaching a calc2 class in the fall. We will see!! : )
blackpenredpen the next year i will see integrals on our tests and i need a bless from Pitagoras to pass these exams
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)
I did the differentiation! Find it here! th-cam.com/video/as1vk0IuAHA/w-d-xo.html
Glad you enjoyed yourself with that. This is a great review of a lot of techniques.
here i am watching 30 minutes of math porn and not knowing wtf is going on
Clement Tan isn’t that the case when watching regular porn too?
Жиза
please check the answer by differentiation
Watching this made me very relaxed. You sir deserve a subscribed!
You're videos are awesome! Please keep posting :)
When title says easy and time says half an hour
🤔🤔🤔🤔🤔🤔🤔😱
Cringe
Can you make some videos about the strategies of choosing the right integration technique for different problems?
Bon Bon will try.
That was a really enjoyable lil’ video. Thank you, it was a nice little refresher! 🙂
An excellent video, explained clearly. Really enjoyed watching the video and even had a try myself after watching. Great job.
我非常喜欢这个视频关于积分。黑笔红笔老师的解释清楚！看到了这个视频我自己试一试解决这个积分！
Good. this is a high level problem in my sheet .
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...
oscarjd74 OH WOW!!!! YOU ACTUALLY DID IT!
NEAT, instant screen saver ^^
How cool iz dat?! HAHAHAH
It's also expressible in terms of "the" hypergeometric function 2F1.
This is just what I needed for my summer.
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
BlackFiresong wow nice!!! I will check it one day too.
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!
BlackFiresong I am very glad as well!! Thank you for watching my videos :)
You earned yourself a new sub
Thanks sir .
Glad to hear! Thank you!
Great video! Have you ever done a video on something like integrating root(lnx) or the something of the sort? My favourite of your videos are ones like these, after having a go and failing miserably it's nice to see I wasn't missing anything *too* obvious haha XD Keep up the great work!
Thank you dude, your explanation is very good, efficient, to the point, best of lucks
saultube44 thank you!!!
This does turn out to be a monster of an integral "doesn't it" :-)
Yea, isn't it?!
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).
This is so great! I wish I still had the "mathematical muscle" to do this myself. Maybe one of these days...
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
@@thelegendofme7520 Aaany day now... ;)
very very good video and very satisfying to have a clean solution in the end.
Wow, impressive stuff. How did you initially learn to solve it? Copious amounts of time and errors? Experience just gives you the intuition to know when/where/what to substitute and what steps to take? More than anything, I'm just curious how people like you navigate through problems like these. On my old calc 2 exam, there were relatively difficult problems, but I could kinda just look at em and get a feel for how to solve it in my mind, but this seems like way too much to do a mental run through from start to finish.
Either way, great video.
Great, now integrate (tanx)^1/5
Please make a video about the nth root of tanx
yes i agree
Yes, that'd be great! :)
I want to see that too
tan(nx) ^ (1/n)
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.
Cara, impressionante! Parabéns pela loucura de resolvê-la.
I'm so happy to see a "BIG INTEGRALS NO SHORTCUTS" playlist, will watch them all
"When in doubt, use horseshoe mathematics."
You too saw the video!!
I see, you are a man of "NO U" culture here!
pure beauty...!
Thank you!!!!
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.
I love your videos!!
do the integral of sqrt(tan(cuberoot(tanx)))
Kyle Farias Just use numerical integration on given bounds
I was kind of hoping to see you dancing in celebration chanting "One Take!" at the end
who knows maybe its 10th take
Notice that I didn't edit this video!
MrQuantum "one take" and "1st take" are different.
Mark Zero true. One take for this tho. I think it was my 3rd take bc my intros weren't good enough.
Mark Zero k
seems like a deep breathtaking moment when you got the answer to be this long...
Most elegant integral I've seen so far,thank you sir
Nothing even remotely elegant about this. This is the equivalent of opening a safe by dropping an anvil on it.
: )))))
Can you do integral of (xtanxdx) ?
Best problem ever!
Tour de force for methods of integration.
I counted eight different tricks.
TI-84 plus showed it correct over:
-2π
Gratulálok, ez a szinte végig helyettesítéses módszer bemutatta, hol kezdődik az elméleti matematika !
now the nth root
yea dog imma need you to check by differentiation
Tumbs up for this ace demonstration !!!
Pretty cool and nicely done! May i request to make a video about integrals of non elementary functions like e^cosx? Very much appreciated if you would.
Okay so you've done sqrt tan x, you've done cube root tan x, can you generalize? Nth root tan x ?
Running a marathon is easy compared to solving this integral 🤓
You are really great sir.
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
It is too long, not too hard. Anyway I doubt anyone can do it in any exam without making a small mistakes ☺
it's like running a marathon (well, almost...)
Dr. BalckPenRedPen, please check the answer by differentiation :)
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
Jesus Christ! With this you have won a new follower! Subscribed!
You can't impress a girl with it
sure it's too smart for them....
I disagree. Perhaps your trying to impress the wrong girls.
No you can't impress the girls quite true, but you can impress them with the money you make if you're working in this particular field.
If you can't impress your girl with this stuff...
*you're not talking to the right girls*
Almost all girls like money, luxury cars and spending time shopping. They want M-O-N-E-Y......and their math skills is +....+money+money+money......
...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
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.
This is awesome! Never seen such integral before :O
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).
Florian Bender if you mean 1/tan x, he would write it as cot x
Florian Bender tan^-1 is a standard notation for arctan
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.
Monzur Rahman We're aware, but it's a terrible notational standard.
It's not even a "standard" notation really. Just a commonly used one (and not even as commonly used as the arctan notation).
....It wasn't that bad....it didn't have limits to substitute (hehe ! )
I have tested to diferenciate on geogebra and it works !!
Cool video !!
excellent travail ! Explication en détail
And then you look at the footage, and you realize you didn't press record...
Everytime he says 'something' I hear 'sensei' *_*
Samarth Varshney or... passdee instead of positive. Forgive him, neither him or me are english ppl
Don't look, sempai. Baka baka!
For anyone wondering, the constant to make them equal is pi * sqrt(3) /12
wow. you're amazing! i've found it satisfying to understand the solution of the integral of the square root of tan x. but now my question is (and i've been looking for a solution to this - mathcad used erf which i don't get) can you please show the solution to the integral of the square root of sin x, and the solution to the integral of the square root of cos x.
please. i wish i had you as my math professor because you don't make shortcuts in showing the steps of the solutions!
thanks!!