Integration using U-Substitution

[izelkay]

"Hey baby. I'm gettin' tired of my girlfriend. Can I do a you-substitution? ;)"

[fadedBl00d]

hey, for the last type of problem my teacher wants it simplified further, would factoring out (x+2)^(3/4) and then distributing the fraction and factoring out the fraction be incorrect? After I did that i got (4/21)((x+2)^3/4)(3x-8), is that correct?

[kattunluver16]

I really appreciate what you do :)

[mushuhead88]

thank you so so so much. i understand this so much more now

[NoDoubtFilms]

Thanks for taking the time to do all these videos. Every time I don't understand something, you always seem to have a video about it.

[claire383]

Thanks this was super helpful! :)

[Dubbidubdub]

Sorry, but I'm very new at this and confused. For example one, why do you find d/x of x^2 + 4 if you are integrating, not differentiating. And why is is 2x d/x, not just 2x. Why do you need the d/x. If you told me to differentiate x^2, I'd just say 2x.

[AndromedaGalaxy2903]

Thank God for you! I just wasn't getting it, but I understand now! Ah! So much better!

[Mattew10922]

your the best!

[93JEANPAUL]

thank you so much. In these videos and in your teach I find the hope to got my math exam passed :)

[andesinoctober]

I can see clearly now the rain is gone!

[playboyjenna]

Im lost. Second example, what happen to the -du. Just disappears? If it disappears why even tack it on? Can't we just ignore it?

[Chrismanggg]

..I GET IT. EPIPHANY.

[bigpapas12]

dude!!! thank you so much!!! you're amazing

[lolsofunnyful]

wait... so does the du just disappear at the end?

[Desolair1]

@lolsofunnyful It goes away when you integrate it.

[t0r4g0wn4g3]

@lolsofunnyful Yes. When you take the integral, the differential goes away. Same as how the integral of 2xdx is x^2 + C.

[A213ondeck]

Thank you

[afro24allday]

is there a vid with definite integrals?

[WindBreaker77]

Anybody else had that awesome moment when you finally understood?

[patrickJMT]

@WindBreaker77 i have had many in my life :)

[xDoctorWho]

I don't understand what happens to the DU. Does it simply cancel out, for lack of better terms?

[94NFK]

Wait, I feel like this is a dumb question, but how did he get u^(3/4) at 8:10?

[94NFK]

@94NFK Nevermind! Just noticed someone asked the same thing an hour ago! Thanks for this video, you just saved me from failing my calculus quiz tomorrow... I'm a little mad I haven't watched these before, my teacher has been talking about this for days but it never clicked until I watched your 10 minute video! THANKS

[Celletto13]

@msshort106, he split the fraction in 2, so u/ u ^1/4 - 2/ u^1/4, he flipped the bottom to the top so it became negative. Than subtracting u ^3/4 and u ^ -1/4.

[Celletto13]

@msshort106

[mshort106]

How did u get that part at 8:16

[mshort106]

my bad. I found a formula sheet with the wrong integrals on it sorry

[mshort106]

why are we using -du when the derivative of cosx is just sinx?

[laurabustamanteloaiz]

what happened to the du when u took the antiderivitive after u did the u substitution?

[BikutaHo]

Omg thankless

[1992crimsonnoble]

:O wow nice video bro, i like the page effect, i do sort of the same thing with my integration tutorials, they are silent, but good help nonetheless

[marter544]

Thanx 100000 times.

[rt36crazyfists]

Good Video, thanks

[russ4553]

you are so wise, sir.

[NotAllanHuynh]

Night before a midterm. All feels hopeless. PatrickJMT. Never fails.

[patrickJMT]

@NotAllanHuynh good luck! :)

[LSGBeats]

@NotAllanHuynh good luck! :)

[erectance]

@NotAllanHuynh same here

[fistful0fst33l]

ZOMG U ARE SOOO MCUH BETTER THAN MY CALCULUS TEACHER LOL!!!!!!! I SHOULD JUST NOT GO TO SCHOOL AND WATCH YOUTUBE VIDEOS ALL DAYH ON MY IPAD LOL!!!!!!!!!!

[fistful0fst33l]

@fistful0fst33l btw thanks for the video patrickjmt. i hope you find the above comment funny

[tim9mlinaric]

these videos are awesome thank you



[tv101057]

thank you so much for your videos!

[Disney1466]

Tnx 4 the video :). I've already kinda gotten the hang of it but the idea of using a negative "du" and the last example were really helpfull, so thank u very much ^^

[0p0a0s4]

Man I was so confused because my teacher doesn't explain very much since it's an "AP" class. Well this is my first years in any AP class and your video have managed to get me a B in his class. THANK YOU!!!!!

[mage1413]

i said this in grade 9 once, and I'll say it again in my first year uni class....You are the best! most people would say that you're adding on to my teachers help, but I say that my teachers are just adding on to your help :)

[ECU7]

I should of found this video f*cking earlier. Thanks dude, it was good.

[emceehamm]

@ECU7 word



[username6333]

Related video " am I pretty or ugly" ???

[dfjndsk2008]

this is great!! I took calculate years ago, now I'm working on my actuarial science exams, which require so much calculus calculations!!! this is such a great review!! Thank you Patrick!! you are awesome!! keep up the good work!

[viadude2011]

Thank you so much, it really helped me!

[Minishglob]

i coundn't figure out what the dx in 'du=2xdx' means. does anyone know what the dx from 'du=2xdx' mean to the first problem (excercise) in the video?

[patrickJMT]

@Minishglob it is the change in x

[patrickJMT]

@Minishglob the infinitesimal

[emceehamm]

@Minishglob the dx is merely Deriviative with respect to X, hence "dx"

[kennethkrist]

@Minishglob When you substitute, you put u = something.

When you got u = something, you can derive the expression with respect to the variable (often x), here using f(x) instead of x^2 as a more general example:

u = f(x) => du/dx = (f(x))'

du = dx (f(x))' or dx = du / (f(x))'

When you got an integral with dx where you choose to substitute, you can use the above algebra and derivation to replace both the core ("Stuff on the inside") and the dx with terns respecting u instead of x.

[kennethkrist]

@kennethkrist The point is following:

You have: dx = du / (f(x))'

That means you can replace [dx] by [du / (f(x))']

Hopefully (this is the point of substitution) you can get rid of any x in your integral because in the above expression you get to divide by (f(x) derived)... Then you should be getting an integral with only u's instead of x and the more complicated the U you choose, the simpler your new integral should get IF you get rid of all the x's...

[louisanal]

The most famous left hand in maths history.

[jhames0214]

again a very helpful tutorial.. =)

I finally understand it!! lol.

[mcr1ash]

thank you thank you thank you i was doubtful but now i get it helped so much with my hw today

[parthpat3l]

thank you. you sir, make procrastination much easier.

[timofei123]

whats the point of having du, why does it just dissappear all of a sudden

[daytonagirl400]

I am so grateful for your videos! It's Day 3 of Calc II and I've been stressing already, but your videos have helped already! I'll definitely be watching more throughout the semester!

[patrickJMT]

@daytonagirl400 come back any time ; )

[gholy2743]

Haha definetly a boss! Thanks for the video, getting ready for calc 3 after a year break.

[hellkid94]

Calculus of a Single Variable is horrible at explaining this, thank you so much

[lovebrazil10]

Thanks for clearing this up for me. So much better than my math teacher.

[csiebler]

Thank you! You're so boss! That third problem helped me so much. I had that x hanging out still and didn't know how to get rid of it!

[pixma321]

This is a awesome video!! thanks!!

[20raeali12]

Thanks so much! This really clears it up. :)

[AnonymityUnbound]

very helpful. thank you very much. :)

[Anoshh50]

dude you are an absolute legend, after my a levels i will definately be donating!

[TheCoolman5500]

thank you very much

just ....just something amazing

keep going teacher keep going we need you

[SM10101010]

Right handed watching someone left handed from first person is really weird..

[TonyqTiger]

multiply it to the power of 100 hahahahahahahahhahahahahahahah

[glennardskynyrd]

On my calc final today, I was stuck on this integral and was stumped on what to do. (X^2(X-2)^1/2 + sinxcosx) dx  I tried u substitution but my answer did'nt come out right. So, if you could give me your input on this problem I'd be very grateful. Your videos are awesome by the way. They are getting me through Calculus.

[timmygofthetree]

Thanks Patrick, my calc final is tomorrow and your videos are really helping me out.

[TheExponentialjoy]

Thanks for uploading. This really helped me while studying!

[simplierickah]

What if your numerator was anything but x? For example, 3x^2/sqrt(x^3+1)?

[jboidaman99]

your handwriting gave me a massive NRB.....(non random boner)

[isitvintage]

using sharpie to do math...what a boss

[loonybin]

OMG. I SPENT HOURS STUDYING MY STUPID WORKSHEET ON THIS AND YOU CLEARED IT ALL UP IN MINUTES. I LOVE YOUUUUUUUUUUU! :DDD

[mamu7mich]

@patrickJMT shouldn't you be saying that that we would take differential of u not the derivative?? my teacher says that we would take differential of both sides...

[patrickJMT]

@mamu7mich yes, that is actually correct, we are calculating a differential

[CyberViewer007]

When you integrate how come the "du" disappears? At roughly 5:40?

[dianalovesya]

You are amazing! Your videos help me out a lot :)

[haafizah786]

my goodness..your handwriting is sooo sexyyy...

[Perulaiz]

how is u/u^1/4 = u^3/4? im stuck in that part....someone help!!! :D

[patrickJMT]

@Perulaiz when dividing, you subtract exponents. 1 - 1/4 = 3/4

[Perulaiz]

@patrickJMT Alright got it now, thanks a lot :)



[fo2shawy100]

@Perulaiz when you devide , you take the difference of powers

[AliveDog]

Awesome. I hope you go all the way up to DE and linear algebra!

[wakiani]

Patrick JMT plz tell how much money you earn (per month) by youtube?

[jenniferru]

@wujiway thank you! Idk how i didnt see that haha :)

[irnotdum]

I haven't checked any of your newer videos, but based on this one, you should look into some kind of pop filter for your camera so you don't get the heavy "puh" sounds in words like suppose. Just an idea! Thanks for the videos.

[TheAwesomeNegro]

You're an absolute life saver! I'm attempting to switch from AB Calculus to BC Calc at the end of this semester, and these videos are really helping me catch up on some of the stuff I missed out on!

[ilikeyellowsnoww]

You have very nice and tidy writing

p.s thanks for putting this up!

[hathorrox]

you are the best math tutor ever. every person i have ever shown this channel to agrees. i hope you know your videos do make a difference for so many students ^_^ ^_^ ^_^

[ErinMusikk]

You have made my night so much easier! I still don't understand the "why" of this substitution, but at least I know how to do it now! Thanks!

[Sophos999]

I have learned more from you in 20 minutes than from my math teacher in 2 weeks.

[drillfang25]

My teacher always says "We use u, we need u, but in the end we always go back to our x" :P

[ErinMusikk]

@drillfang25 I intend to tell my calculus class this tomorrow. Thank you for making my night. :)

[dpressed]

cabrón vas muy rápido! Cagoendiej!

[jenniferru]

Im confused.. why does u/u^1/4 become u^3/4?

[Korruption666]

What happens to the du? Why does it just disappear in the solution? Does that always apply? I would appreciate the help. Thanks in advance.

[sleepisgoood]

when you do the second example with cos and sin, should the final answer be divided by 5 or 4?

(I'm substituting theta with 'Q')

cosQ^4*sinQ*dQ

=  -(cosQ)^5/5

OR

= -(cosQ)^5/4

isn't there a product rule or something? i forget what it's called, but that's what you did in the first example where it was raised to 100 and then the power became 101 divided by 100...

[dpetrosiann]

for some reason when i try to derive the answer, i dont get the original integral. Any ideas? For the last problem, the one with the one fourth root.

[dpetrosiann]

for some reason when i try to derive the answer, i dont get the original integral. Any ideas?

[opethggah]

what about u substitution with ln inside the problem?

[adaniel140]

Hey Patrick! could you make videos on inverse chain rule please, I'm having a bad time with those, thanks!

[patrickJMT]

@adaniel140 not sure what that is.

[adaniel140]

@patrickJMT My professor call it Chain Rule reversing substitution, and from what I understand is for cases where you have to integrate trigonometric functions with stuff inside for example cos(3x), the solution for that one is 1/3sin(3x) but no idea where the 1/3 came from. I thinks he also uses it for complex cases of U substitution. Thanks in advance =)

[patrickJMT]

@adaniel140 ok, i thought that is what you meant. you use u-substitution. he is talking about this stuff.

[aakerstroem]

@adaniel140 I guess this is inverse chain rule

[gunny0488]

@adaniel140 haha did you even watch the video: u subbing is the chain rule in reverse (thus an integral and not a derivative)

[recabeccakim]

At 5:40 why don't you distribute the negative to the sign before C? Like, why wouldn't it be -(u^5)/5 - C ?

[Solaris989]

two weeks of lectures and i couldnt figure out what my professor was doing. 3 minutes here and i understand it, thank you patrick

[FeelingFreshSon]

so is this just using variables to make things simpler?

[sulmazz]

Thanks Patrick you are so awesome !!

[barbaric37]

my professor went through this so quickly today and I was confused about the whole du and dx thing and how to utilize them. This definitely cleared it up for me, once again! thank you

[MarCeh12345]

Patrick, I love "U" <3

[TheGDoubleD]

@MarCeh12345

haha i see what you did there..

[sulmazz]

@MarCeh12345  Good one :)

[Cancer98765]

When you have -∫u^4du and you go to

-(u^5)/5+C is this

-[((u^5)/5)+C]

or is the constant constant and thus not changed (not affected by negative sign)

[FlyTheKidd]

Thank you kind sir ! If only my professor was as clear as you. #ThankYouBasedGod

[kalinx31]

this video is a lifesaver

[musicianche]

I love your voice, it's so nice and pleasant and unpretentious. Thank you so very much for these videos--they've helped a LOT.

[antoboy99]

you make this so easy to understand thx

[diehardopethfan]

hi,this is pranoy from india sir,pleasure learning from you sir,great tech. and skill :)

[kgfreak]

My calc bc teacher goes too fast, and this video just summarized a whole hour's lesson in 10 minutes. Thanks!

[SaFiRe219]

Thank you so much! I adore my ap calc teacher, but it's so helpful to be able to watch these videos at home. thanks again

[HackerzInc]

im subscribing!!!

[toda9008]

im confused if my du and dx dont match what do i have to do to make them equal so i can replace dx with du my prof isnt really clear & cant understand him all that well plz help

[kgfreak]

@toda9008 You don't have to get du = dx every single time..

[johnrfeeney]

excellent teaching - methodical and precise

outstanding!!!!!

[DuckODuckProductions]

Thank you so much for your help!

[maknzofficial]

Fantastic help. Thanks!

[Hypna88]

You have a great handwriting Patrick

[patrickJMT]

@Hypna88 i try to keep it legible when i make videos ; )

[lillibeth13]

@patrickJMT Something my math professor told me that really resonated with me is that u-substitution only works when you have the derivative of u, du, as a FACTOR. As soon as I heard that, I know when u-substitution would work and when it doesn't =) !

[patrickJMT]

@lillibeth13 well, i think it is a touch more complicated than that, but it for sure works in that case

[xXTheDeathReaperXx]

Love your videos man but I find them to be too basic, please do some really complicated and advanced stuff, university level stuff :) I'm really impressed by the way your teach though.

[TheAngryDuckman]

24 people are math teachers.

[patrickJMT]

@TheAngryDuckman i still dont understand why everyone is always hatin' on their math teachers. i used to be a teacher. this attitude is why i no longer teach.

[MrAthanz]

@patrickJMT Its not the teachers that students have a problem with, its the way everything else is setup. What teachers need to do is adapt to the changing world and to adapt how students best learn, one-to-one communication either it be personal or online videos. The idea that everything is going to be thrown at you and your expected to know it all on day one doesn't work. Your type of videos work, they must adapt to that or change the old system of education. By the way, thanks for the videos

[patrickJMT]

@MrAthanz how can a teacher give one to one instruction? there are too many students and not enough teachers. mention the idea of raising taxes to hire more teachers and everyone goes crazy. glad you like the videos though : )

[xXTheDeathReaperXx]

@MrAthanz for me the best way to study maths is by a lot of practice and my lovely Cambridge textbook, if I have a textbook, I don't need a teacher :) My teacher at school hates me because I don't give a shit about what she says because I'm always ahead of everyone in my class. I do Maths Extension 2 which is the highest level of maths you can possibly do in high school, year 12.

[AunShovah]

@patrickJMT You, sir, are still teaching

[jacoki]

I went from not knowing jack to aceing my test in 2 hours thanks to you

[TheNumber2Pencil546]

how did you get the u^(3/4)?

[Suzn419]

@TheNumber2Pencil546 Ya thats what I was wondering, blew right over my head, i cant figure it out either..........

[xXTheDeathReaperXx]

@TheNumber2Pencil546 1 - 1/4 :) When you divide u by u^1/4 you subtract the powers which is in this case 1 - 1/4 = 3/4.

[TheNumber2Pencil546]

@xXTheDeathReaperXx thanks for the reply :)

[xXTheDeathReaperXx]

@TheNumber2Pencil546 No Worries :)

[LetsGoECU1]

how many teachers have advertisements on their math teaching videos. baller. Ps thankyou for having an accent that isnt indian and understandable

[Skara555]

For the first question. what was the point of differentiating the u??

[pepteamsergi09]

TY

[JayZ000radio]

In Greece these are high school mathematics! xD I'm 18 and I just said to get some extra information about integrations for the following test on Monday!

[patrickJMT]

@JayZ000radio high school math in usa, too. high school math in most places.

[phenethylaminedreams]

@patrickJMT Not in public highschools in florida. I'm 17 years old and I do calculus when I get bored in Geometry class. Kids think I'm a wizard because I know what the Taylor series is. I feel so cheated. Not only was I entirely screwed over in my math classes and forced to repeat classes that I passed, the education isn't up to par even when I am in the proper class (which is only as of this year). I want to get into MIT. My grades aren't the best as an underachiever, but I <3 higher math.

[JaySmith91]

@patrickJMT High school maths in UK. Integration appears at A-level, age 16-17

[MrValzen]

@JayZ000radio

High school maths in UK aswell

[TheNumber2Pencil546]

you make my professor look like an autistic first grader

[Dredangel32]

what happened to du and dx? do they cancel out?

[Wylldsico]

you are unbelievable!

[etfirljcei]

you can do what you did to the X, to any fuction left not equal to the derivative you got from the initial U?