Understand u-substitution, the idea!

[@srpenguinbr]

I remember the first time I watched a video from your channel. I barely knew how to differentiate functions. When you did the u-sub, I didn't understand a word you said because I was used to thinking dx was just a notation that could tell what I call variable. I'm much better in calculus now. Thanks for making me a calculus enthusiast, together with 3blue1brown.

[@blackpenredpen]

This is amazing to hear!! Keep up the good work and one day you will be great!

[@ankitaaarya]

@@blackpenredpen how dx is not just a notation

[@birdboat5647]

@@ankitaaarya en.wikipedia.org/wiki/Differential_(infinitesimal)

[@brodierussell74]

I guess im asking the wrong place but does any of you know a trick to log back into an instagram account?? I was dumb lost the login password. I would love any assistance you can offer me!

[@srpenguinbr]

@@brodierussell74 if you cannot send a recovery email os SMS you've probably lost it

[@rizz.boy47]

His voice makes it easier to pay attention for some reason

[@guitardudee777]

my calculus professor is scary good, but he's not good in communicating mathematical intuition. We are always wondering how this became that. You, sir, are the complete package. You communicate mathematical intuition well and can explain everything, at the same time, you are scary good.

[@dmorgan0628]

I know what you mean I had a professor that knew every aspect of Calculus but would be annoyed by someone asking precalc questions like we should have all of algebra and trig mastered coming into his lecture.

[@vimuth_04]

Wow its been 5 years how’s it going 😁

[@dylanrelatable]

@@vimuth_04 Hello 😅

[@infinitymfg5397]

This was as really good explanation.

[@blackpenredpen]

Thank you so much

[@xsytrance]

This was sooooo good! You blew my mind when you showed the connection between the chain rule and u-substitution! I've always had a problem choosing a candidate for the u. Thank you very, very much for this explanation!!

[@Anuradha-cc1hh]

Bro, you're amazing! You actually know how to explain a concept. God bless you with money. You saving dreams and careers out here!

[@armanchowdhury1415]

The best, most clear and concise explanation I have ever heard. thank you too much, you are a great teacher.

[@blackpenredpen]

You're very welcome!

[@barthennin6088]

I finally "intuitively" understand "u" substitution for integrating! ..In High school and university, I successfully used u-sub to integrate but it was 'mechanical' w/o really understanding what was really behind it...Never realized it was just the chain rule in reverse! Yay!

[@n_2619]

By far the best explanation of u sub! Today in class my teacher tried to teach us this method and to say she destroyed the whole idea would be an underestimate. A large part of my skills in mathematics i owe to you! What an amazing teacher, keep going!

[@machoslothman]

great explanation. trying to review material before i start my calc 2 course. you helped me bring my 50 up to an 80 in calc 1 this semester, thank you so much!!

[@dmorgan0628]

In two years you will have so many views and subscribers especially since you continue to make so much content. I bet your students love you. I think Professor Leonard has some competition now haha

Bear down!!!

[@eseasoro7251]

U were right

[@kepler4192]

You are very much correct

[@theartofmusic05]

Man appreciate you for a living I have seen 60 videos about the substition rule of integral and I didn't understand nothing until I saw your video thanks bro I am 15 now years old and I really understand them

[@robertadam512]

such a great explanation, thank you very much!

[@drakeaske9784]

Awesome teacher! I bet your students do very well after seeing how easily you simplify things and show the connections

[@ramyhuber8392]

Wonderful, just watched for the first time. Clear, well presented, easy to follow. Plus I like how you use the marker...

[@d7neu250]

I haven't taken Calculus for the whole semester ... I'm a math student but I've been lazy and didn't really do much in college.. But I'm surprised I actually guess every steps you take and know the answer .. That was a brain refreshing!!! ... Thank you too much and I hope I can get back on track!! ❤❤👍👍👍

[@blackpenredpen]

That's great! I am glad to help

[@MrCmon113]

Oh man, you'll be fucked. One tip: Look up the most important inequalities and series. Calculus is all about pattern recognition.

[@taijmohabeer4515]

oh my god, you are genuinely an incredible teacher. i am fresh out of my o levels and am planning to take further maths and this is incredible

[@blackpenredpen]

Thank you!

[@OliviaBenFranklin-jg7ou]

You're the least confusing calculus youtuber I've encountered! Thanks for these videos!

[@TheZmoliver]

You're the king, man. Thank you once again. I was just watching some of these as a refresher but they really help refine my instincts (if that makes any sense) to where this stuff just becomes more intuitive. Snap! Just like 2nd nature.

[@TheSuntriber]

Once again you succeed in explaining what my textbook doesn't! Thank you!

[@dexio85]

I wish you were my math teacher in the university. Love your videos.

[@blackpenredpen]

thanks!

[@ahmeraymen2006]

u rock the calculus. man you save my brain and energy to understand the two basic concept

[@keenaneisermann883]

Simple explanation. Thank you so very much. You have made me so much more confident in understanding and using u sub. You should be very proud of your work!

[@maznurahman2422]

I love you very very much.I am a physics undergrad student.Your videos are helping me a lot.

[@Kart-sl2qq]

Best Video to understand as a calculus student myself, great Job!

[@Treegrower]

Very clear explanation, thank you.

[@frankharr9466]

I agree with my caculus teacher, the hardest part of calculus is all the algebra. That seems clear and logical.

[@MrCmon113]

Nah, the hardest part is finding useful upper and lower bounds and proving stuff like continuity that always require a trick.

[@black_jack_meghav]

The hardest part is overcoming the illusion of difficulty.

[@palmtrees9474]

You are a genius man! Hats off!

[@pwnd785]

The second one can also be done as f’x/fx

[@StuartSimon]

I had so much calculus in high school so as to get as far as what was just before L’Hopital’s Rule. When I was shown how simply integration by parts was derived to undo the Product Rule, it suddenly became clear to me that u-substitution was used to undo the Chain Rule.

[@jarikosonen4079]

This is probably one of the best methods (along with D.I. method) to make integration easier... but finding right 'u' can be problem sometimes.

[@josierodriguez9278]

Suddenly everything makes sense ….. THANK U !!!!

[@locutus7855]

excellent - the IDEA behind u - substitution. Bravo

[@GreaseMonkey33]

Bro you just helped me so much, what an absolute unit my guy

[@vishnukaliugavarathan5459]

was looking at the textbook for couple hours and was not able to solve a single question because it didn't provide any useful information on how everything is related now I am able to do the homework without looking over any examples just through 1 of your videos.

[@awya1467]

Isolate the dx seems like a real nice trick!

[@mauricioconejo102]

Thank you! I was struggling understanding this subject!

[@tobiasjdcolvin]

Wow this is the first U sub video that made it click for me, thank you!

[@Beeboysquared]

So in the 1/5x-2 example, and others like it, setting u equal to the whole expression gets rid of the constant term when you differentiate. That's useful!

[@Infinitesap]

I simply love your videos. Great explanations.

[@ehatipo4598]

Amazing! heading down to the next video.

[@andreamontano2621]

excelente vídeo, muchas gracias, saludos desde México!!

[@blackpenredpen]

you're welcome!

[@tejaschakranarayan2760]

You are a genius i often watch ur videos n guss what?? I understands very quickly.. 👌👌👍👍👍👍 I love ur videos a lot ... Cheers to u👍👈👈

[@albob8458]

Wow, I instantly understood u-substitution. Very clear and very concise!

[@ysmxysmx3292]

this is my goat guys❤️

[@m3lng3]

multiplying by d/dx os inside for chain, dividing by d/dx of inside for u - sub

[@rubensf7780]

Helpful

[@adamkangoroo8475]

u're great :D

[@alexanderpoltzer8885]

Adam Kangoroo ha ha ha good joke!

[@kaushikroy1747]

I Have One Doubt Sir May I Ask??

[@ryzenandrewgarcia657]

How about in these terms: the Chain Rule is post-derivative while the u-substitution is the pre-derivative, following its connection.

[@iternai3872]

For the first integral, when you divided by 4x^3, wouldn't that mean x can't equal to zero?

[@pigchopORIGINAL]

Fantastic explanation.

[@SinisterPrince]

Thank you, bro! This helped me a lot.

[@elendor3428]

Fantastic explanation

[@oh.smetanka]

Superb explanation!

[@ebadrahman1290]

simple and informative

[@isaacneilton3497]

Adoro os vídeos desse cara

[@doodelay]

Woooooow it's all becoming clear to me now. I did not see the connection to the chain rule.

[@zabul4423]

u r best teacher. isn't you

[@LepusCompositions]

very helpful video. thank you :DDD

[@protocolwonder4558]

Great explanation

[@Headerman300]

What is the first integration technique? How many techniques exist? Great video bprp i love your work

[@KevinJonesPandaas]

This is speculation, but it probably is the power rule of integration (for monomial, add +1 to degree and divide the term by the new power). It could also just be “know your basic derivatives”. As for the other question, I’m not sure. As many mathematicians say, “Differentiation is a tool, while Integration is an art.” There are the big strategies, like U-Sub, Trig-Sub, Integration by Parts, and Taylor Approximations, but solving an integral is like a map- the individual examines the routes and uses their knowledge to show the quickest path.

[@rickdoesmath3945]

The first technique is calculating the integral from the definition, and it actually works for all the elementary functions (like if you have monotonicity then it's an easy win)

[@isi6402]

This help me in A level Exam

[@rob6129]

Thanks for this video, now u-substitution seems less esoteric to me ^^

[@stephenfreel2892]

I always thought multiplying dx/du was geometrically kind of like dilation of another functions integral such that it matches the integral of the original function

[@debopamsil6965]

Use the chen lu

[@zidanutomo326]

"Let me show you" Proceeds to show 'U'

[@johnedwards887]

Thanks!

[@jeena563]

Thank you so much to be my teacher

[@ratnarajwora2674]

How to find the area under the curve x^4 + y^4 = 2xy

[@carvelbell181]

excellent.

[@BlackZeus1990]

Thank you

[@lorenasiu3113]

Thank you so much

[@RadulovicDragan]

Bravo!

[@adrianmacias9144]

Where was this video when I needed to learn this before my chapter 5 exam 🤣

[@whoppers7778]

you are #1 !!!

[@zeyuanluo9707]

I get the technique... but I cannot visualise what is going on graphically when we do the substitution. When we integrate a function with respect to dx, we are breaking the area under the function into many pieces of width dx and finding the area of each piece and then take the limit of the sum as dx becomes 0. In this case dx is constant so this is pretty intuitive. But clearly du is not constant as it changes with x. For example in the first example, du=dx*4x^3, and we are integrating with respect to du. To me, this doesn't make sense because how do we integrate with respect to something that is not constant? Would appreciate if someone can give a visualisation of what is going on (graphically) when we integrate by substitution.

[@robmarks6800]

zeyuan luo how is du not constant? dx is constant, and the 4x^3 will cancel out with some of the integrand, for the substitution to result in some new function

[@ILikeFeelingElectric]

zeyuan luo When you’re integrating, the function on the inside is the same. You’re just changing the form of the function, and changing what variable you are integrating in terms of. So, it’s the same area under the curve, but of a function that looks different than the original.

[@kubinn7989]

nice vid so helpful

[@ohmaga-wn6pr]

become calculus professor at Fluminense Federal University please, come to brazil, we at my class love you so much man 🇧🇷 🇧🇷 🇧🇷

[@vrowniediamond6202]

Just realized I have the same book... Well thanks Mr! :)

[@zomisintu]

May I know which book is that? Thanks

[@mohsinashfaq101]

Great explanation but how do we know which one is 'U'????

[@andregosteli2177]

Very nice!

[@anonym4162]

0:40 Horse power

[@benjaminknudson5997]

Isn't it?

[@ishaanvatus3536]

It is, Isn't it?

[@polyblankas]

MUCH LOVE TY

[@Anonim01089]

So cool!

[@higherle-bi2yi]

thx

[@pulanridick7040]

thanks man!

[@YusufKhan786]

So when you integrating you actually multiplying by the dx at the end? Doesnt the dx at the end have nothing to do with the sum? Is it not just there to help identify the variable of integration? Please explain

[@snillie]

Yeah, the dx does actually represent a quantity being multiplied! If you think of the integral as giving you the area under some graph, you can imagine approximating this area by adding up lots of rectangles side-by-side to each other with a certain width (which we can call dx, standing for change in x, since this is also the change in x of the horizontal position of each rectangle) and whose height just touches the graph of the function you're integrating. Then if you imagine letting dx approach 0, getting smaller and smaller, this rectangle approximation should get closer and closer to the true area, since you're chopping up the area into finer and finer rectangles. So what the dx in the integral truly represents is the behaviour when you let dx approach 0. If you want a clearer explanation of this with visuals, I'd highly recommend 3blue1brown's Essence of Calculus series. It'll help clear up a lot of "why" questions in calculus as well as just this one :D

[@ValidatingUsername]

Man I am digging deep to rationalize this even though I get it from just a memorization standpoint but I have so many issues with it. The point of integrating or deviating a function is that the result is useful and equates to something. With that being said that value is equal to the operator denoted by the integral sign sandwiched by the dx. So there literally is a dx as soon as you try to integrate to obtain that value or d/dx when taking the derivative. When you u sub the x^4 you’re finding dx for that function the same way choosing 4x^3 would result in 12x^2 dx and subsequent dx = du/12x^2. But that wouldn’t be useful if you’re trying to change the base of the integration operator from dx to du because it would simplify to int{ x/3sec^2(x^4)du right?

[@llennzo]

x world to the u world. Got it!

[@exilitygamin3388]

How to know when to use this method!

[@Lerky]

this dude saves more grades than teamtrees plants trees

[@rohanvenkatesh9643]

2:50 we U-sually

[@aashsyed1277]

use the chen lu!

[@archangel1060]

w video thank you

[@dxmady9500]

"Are you doctor yet ?" blackpenredpen's dad.

[@ngsbsad5502]

Guys can someone tell any tips on when will i know if i need to use this coz im confuse when im solving with the basic integration especially if it's a hard problem with square roots

[@shouu000]

How would you differentiate the function with the absolute value included?

[@carultch]

Unless it is a special case where the absolute value signs are ultimately irrelevant, the answer eventually becomes a piecewise function. For instance, d/dx |x^3| = piecewise 3*x^2 when x>=0, and -3*x^2 otherwise. By contrast, d/dx |x^2| is still 2*x, because the absolute value signs are redundant (at least for the real numbers), as the original function already is always positive. Another example is d/dx ln|x|. This one we KNOW is 1/x, which is valid for both negative x and positive x. But why? Initially, it may seem like a coincidence, that all it takes is absolute value signs to reconcile the integral of 1/x, as the integration operation cuts the domain in half. But what is really going on, is that the +C is arbitrary, and is different on both halves of the function. If you let the +C include an imaginary term, left of the origin, you'll see that ln(|x|) + C is really the full complex log, when the +C can change upon crossing the origin. You can take the log of a complex number, and it is ln|x| + 2*pi*k*i, where k is any integer.

[@gameliadeti2967]

Sir please why is it that, after differenting sec square, the du disappear?

[@comprehensiveboycomprehens8786]

This is legit! :)