OK, I checked the answer and it was correct! kzread.info/dash/bejne/n4mMxsmSZbDLdco.html Happy New Year!!!

@notnilc2107

5 жыл бұрын

I approve.

@alexsanders7303

5 жыл бұрын

Lol, just finished the vid and relaised this

@marziyaali7962

4 жыл бұрын

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

@pongwang9893

4 жыл бұрын

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

4 жыл бұрын

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

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

@davidkippy101

6 жыл бұрын

Sheev Palpatine Saw the comment, liked for the name

@blackpenredpen

6 жыл бұрын

Sheev Palpatine I just had to pin this comment.

@levi4328

6 жыл бұрын

oh no, don't give them ideas

@sorryperson92

6 жыл бұрын

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

@user-bv3ed1cn7w

6 жыл бұрын

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

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

@blackpenredpen

6 жыл бұрын

BT7M yup

@isaacormesher2851

6 жыл бұрын

blackpenredpenbluepen

@Anonymous_Poetry

4 жыл бұрын

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

@booga9584

4 жыл бұрын

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

@midhun.m4963

3 жыл бұрын

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

Check the answer by differentiation

@jeffreycanfield1939

6 жыл бұрын

You mad man

@S-Matrix

6 жыл бұрын

You'll break him

@SteamPunkLV

6 жыл бұрын

I didn't understand the joke until I saw the answer XD

@federicovolpe3389

5 жыл бұрын

Avi Mehra The mad lad actually did it

@nellvincervantes3223

4 жыл бұрын

Integrate it again.

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

@dhruvkaushik4872

3 жыл бұрын

BRUH

@StoryTime-jo6ij

3 жыл бұрын

xD

@bananoramatfw

3 жыл бұрын

You're a monster

@asparkdeity8717

3 жыл бұрын

That’s easy

@dravyamehta6180

Жыл бұрын

​@@asparkdeity8717 yeah ok

You're going from blackpenredpen to 3blue1brown

@blackpenredpen

6 жыл бұрын

How so? His vids are way cooler

@Number3pt14

6 жыл бұрын

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

@davidkippy101

6 жыл бұрын

blackpenredpen Because of the color markers you are using

@blackpenredpen

6 жыл бұрын

blackpenredpen and sometimes blue : )

@NoNameAtAll2

6 жыл бұрын

blackpenredpenbluepengreenpen

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

@blackpenredpen

6 жыл бұрын

yoav carmel lollllll nice catch!!!!

@blackpenredpen

5 жыл бұрын

Android Ninja yup

@yrcmurthy8323

5 жыл бұрын

Wow

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

@Vibranium375

2 жыл бұрын

Lolololol

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

6 жыл бұрын

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

@manuelbonet

6 жыл бұрын

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

@monzur1947

6 жыл бұрын

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

@aysikl

6 жыл бұрын

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

6 жыл бұрын

Maybe?!

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

@blackpenredpen

6 жыл бұрын

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

@iconoptixx

6 жыл бұрын

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

@Queenhideyxo

5 жыл бұрын

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

4 жыл бұрын

After that start using ♤♡◇♧¤▪☆

@hamiltonianpathondodecahed5236

4 жыл бұрын

How about हिन्दी

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

@kamarinelson

6 жыл бұрын

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

6 жыл бұрын

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

@eroskuikel9688

5 жыл бұрын

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

5 жыл бұрын

Kyro well Oh yeah..

@surenmoodley7744

3 жыл бұрын

Lol that's sadistic!

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

6 жыл бұрын

Riley Wells my pleasure!!!!

@leif1075

Жыл бұрын

@@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.

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

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

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

6 жыл бұрын

Natalie Euley thank you Natalie!

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.

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

@hauler-hx6gw

5 жыл бұрын

Mr. Gentlezombie spoiler alert

@aneeshsrinivas9088

2 жыл бұрын

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

@mr.gentlezombie8709

2 жыл бұрын

@@aneeshsrinivas9088 D'oh!

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

6 жыл бұрын

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!

@blackpenredpen

6 жыл бұрын

200%productions thank you!!

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

2 жыл бұрын

Fetus?

@JMZReview

Жыл бұрын

Bro really spelled it with an o 💀

@General12th

Жыл бұрын

@@JMZReview diarrhoea

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

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

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

Can you check the answer by differentiation ?

@blackpenredpen

6 жыл бұрын

Pedro Bessa maybe one day :)

@nationalstudyacademykim5030

4 жыл бұрын

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

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

@nestorv7627

6 жыл бұрын

Mace Jr there is no dislike now

@aceeternus4027

6 жыл бұрын

NestorV S Hhh he couldn't do it.

@ZyloSol99

6 жыл бұрын

Nah two people did.

@busTedOaS

6 жыл бұрын

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

@hamiltonianpathondodecahed5236

4 жыл бұрын

Now 5³ dislikes

Fantastic job of explaining every step!

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.

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

@delta2884

3 жыл бұрын

And professor deducts 1mark for that

@invasion8318

3 жыл бұрын

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

@dzlcrd9519

2 жыл бұрын

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

@user-lh5hl4sv8z

2 жыл бұрын

Calc II + Calc II

Could you check the answer by differentiation?

@moregirl4585

6 жыл бұрын

no

@awawpogi3036

5 жыл бұрын

yes

@banana6108

3 жыл бұрын

Maybe

30:40 differentiASIAN

@particleonazock2246

3 жыл бұрын

Lmao

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

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

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

@nestorv7627

6 жыл бұрын

I think impossible

@aceeternus4027

6 жыл бұрын

NestorV S I thought you could integrate anything you wanted

@RubALamp

6 жыл бұрын

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

6 жыл бұрын

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

@sinistrolerta

6 жыл бұрын

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

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*🥳🥳

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

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

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).

Please differentiate this to get back to cuberoot of tan x

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

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

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

6 жыл бұрын

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

I'm worried for you.

@blackpenredpen

6 жыл бұрын

MistaTwoJeffreyTwenty Yaay U should worry about my students

@jeffreycanfield1939

6 жыл бұрын

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

@blackpenredpen

6 жыл бұрын

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

@JorgetePanete

6 жыл бұрын

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

@Metalhammer1993

6 жыл бұрын

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)

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!

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

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

@kibayuuto6634

6 жыл бұрын

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

@suyunbek1399

5 жыл бұрын

Жиза

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

6 жыл бұрын

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

@vj_henke

6 жыл бұрын

NEAT, instant screen saver ^^

@caducoelho2221

6 жыл бұрын

How cool iz dat?! HAHAHAH

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！

Tisztelt bprp ! Ez lenyűgözött, gratulálok.

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

@thelegendofme7520

2 жыл бұрын

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

2 жыл бұрын

@@thelegendofme7520 Aaany day now... ;)

You earned yourself a new sub Thanks sir .

@blackpenredpen

6 жыл бұрын

Glad to hear! Thank you!

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.

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

He did the derivative!!!!!!!!!!!! Check out Fematika's kzread.info/dash/bejne/k6dl2M1pedineKQ.html

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

6 жыл бұрын

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

@BlackFiresong

6 жыл бұрын

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

6 жыл бұрын

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

This is just what I needed for my summer.

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

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

@xamzx9281

6 жыл бұрын

who knows maybe its 10th take

@blackpenredpen

6 жыл бұрын

Notice that I didn't edit this video!

@markzero8291

6 жыл бұрын

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

@blackpenredpen

6 жыл бұрын

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

@xamzx9281

6 жыл бұрын

Mark Zero k

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

@arnavanand8037

4 жыл бұрын

Cringe

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

@ktuluflux

Жыл бұрын

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

Thank you dude, your explanation is very good, efficient, to the point, best of lucks

@blackpenredpen

6 жыл бұрын

saultube44 thank you!!!

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

@blackpenredpen

6 жыл бұрын

Yea, isn't it?!

@JBaker452

6 жыл бұрын

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).

pure beauty...!

@blackpenredpen

6 жыл бұрын

Thank you!!!!

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

This is awesome! Never seen such integral before :O

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

@blackpenredpen

6 жыл бұрын

Bon Bon will try.

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

Cara, impressionante! Parabéns pela loucura de resolvê-la.

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.

please check the answer by differentiation

@blackpenredpen

5 жыл бұрын

: )))))

Not even a single mistake . Great job bro

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

"When in doubt, use horseshoe mathematics."

@craftbuzzwonky4752

3 жыл бұрын

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

Great, now integrate (tanx)^1/5

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

I love how you are so passionate about maths

@blackpenredpen

6 жыл бұрын

thank you!!!

Please make a video about the nth root of tanx

@timedilatesme

6 жыл бұрын

yes i agree

@dicandeo9698

6 жыл бұрын

Yes, that'd be great! :)

@sunriselp849

6 жыл бұрын

I want to see that too

@jiaming5269

6 жыл бұрын

tan(nx) ^ (1/n)

@angelmendez-rivera351

6 жыл бұрын

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.

yea dog imma need you to check by differentiation

Madman. I know you'll have fun differentiating it in your next video.

You are really great sir.

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

@nejlaakyuz4025

5 жыл бұрын

Kyle Farias Just use numerical integration on given bounds

Running a marathon is easy compared to solving this integral 🤓

Tumbs up for this ace demonstration !!!

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

Can you do integral of (xtanxdx) ?

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

I love your videos!!

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.

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

now the nth root

That's was very cool thanks bro!!

bro went through 5 worlds to solve this integral

You can't impress a girl with it

@bmc868

6 жыл бұрын

sure it's too smart for them....

@timstorer978

6 жыл бұрын

I disagree. Perhaps your trying to impress the wrong girls.

@azmath2059

6 жыл бұрын

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.

@General12th

6 жыл бұрын

If you can't impress your girl with this stuff... *you're not talking to the right girls*

@bmc868

6 жыл бұрын

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......

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

6 жыл бұрын

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

@monzur1947

6 жыл бұрын

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

@GrouchierThanThou

6 жыл бұрын

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

6 жыл бұрын

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

@GrouchierThanThou

6 жыл бұрын

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

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.

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 ☺

@blackpenredpen

6 жыл бұрын

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

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

Wolfram Alpha says" you goddamn right boy"

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!!