❖ Integration using U-Substitution ❖

[@patrickjmt]

Hi all! Wanna help a KZbin education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

[@ballerbob388]

I have been using your videos for calc 2, cal 2 for life sciences and now calc 3. your videos have persuaded me to add a minor on my major. as long as you keep singing nobody will get tired of dancing.

[@patrickjmt]

Oh wow, that is literally one of the best comments ever

[@pbrayat2404]

so deep, i saw adele rollin'

[@pbrayat2404]

so deep, i saw adele rollin'

[@linusherr8257]

Baller Bob Would one use the substitution method without using the chain rule? As in the last problem?

[@jackcabral7354]

Baller Bob I

[@robertherrington3379]

When Patrick is explaining a problem. I listen closely. What I hear is the voice of God saving me from my math exams lmfao!

[@TJace50]

LMAO

[@gilbertoaltamirano4543]

You sir, just won the internet.

[@rirecvz]

Robert Herrington LMFAO ! I feel the burn now !

[@TheBlackLodger]

Patrick JMT = the 2nd Coming of Christ. In other words, he's a life/grade saver.

[@David-fj2bx]

Good comment

[@revit.2184]

After a 2 hour class, i'm lost... >.< After a 10 minute video, its a piece of cake! You're just awesome!

[@sxge4751]

this still stands today

[@TheSouthBeachElites]

@@sxge4751 can confirm this is true

[@Haza-rp1cb]

9 years later we all like this bruh

[@jclmoose]

:/ that moment when a free youtube video is better at teaching than a paid college professor

[@naylasantana111]

I feel you

[@tyler681]

Such is life

[@shavuklia7731]

lol i study online mostly. i go to school 30% of the time (only because it's mandatory). learning on stack exchange (online forum for maths) and watching the occasional youtube lecture works much better for me

[@ianmanning4062]

I think you mean a low opportunity cost KZbin video :)

[@SmittyKat]

If professors didnt talk as fast as Busta Rhymes raps then I wouldnt have trouble keeping up lol

[@volejcore3933]

Ok.The world needs more patrickJMT.

[@asurastorm8566]

Hello Patrick. I'd like to thank you for getting me through my first year of Calculus. Your videos are great and helped me understand just about everything I needed to know. You really should consider making a book. I feel the one I'm using right now does a terrible job in explaining even the simplest of problems. On top of that, the examples they give are incredibly easy and don't give justice to the problems in their section. Once again, thank you.

[@nomad6337]

tell me about it, i have to give an exam and the book isn't helpful at all

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@zahraoth8745]

Bro keep that good work up! You are saving are lives!! You are my fav calculus teacher ever!!! ❤️❤️❤️

[@EchoEcho-q4r]

Is there any to connect with you directly for tutoring and help?

[@strongwickarts3294]

Is there any way I can keep in touch with you..or any reference book

[@shukri1724]

​@zahraoth8745

[@NoChance1909]

Why is this 10 min KZbin video better than the 50 min lecture I just had?!

[@lasseskoulindstad8047]

Wow that last example went from 0 to 100 real quick.

[@exekiajq]

Once I get my degree I'm gonna make a huge donation to your channel. I owe you big time.

[@patrickjmt]

+exekiajq can donate on patreon for as little as $1/month. :)

[@HoyaSaxaMV]

You accomplished in less than 10 minutes, what took a professor at a top level university an entire week. You truly have a gift. I am so thankful to you for posting these videos.

[@fuzzygreen3634]

Explained something in 5 minutes that my teacher failed to do in 2 hours... patrick is the best out there

[@OpenPlatformInterests]

failed my first two tests of the semester with a 41 and a 64... i spent my time at the tutoring labs and they didn't work... I then found PatrickJMT on youtube for the 3rd test and managed to pull of not only passing, but actually getting an A on the third test with a 96! I cannot thank you enough for making everything so clear!!!

[@patrickjmt]

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

[@sleepingpetal]

Have you ever consider writing textbooks? I feel most math book writers try really hard to be as unhelpful as possible.

[@ducksoop.x]

Seriously, its like they're trying to fail you.

[@hisheartofstone]

TRUE AF

[@rozikhan2744]

The thing is alot of the material and test questions are based off the textbooks

[@danceartist8203]

They always try to be 100% correct, so their notation is super mathematical all the time, which sucks.

[@LoLIHateMyNameLoL]

I found integrals to be so difficult when I was studying for my exam. Now I finally understand u-subs! thanks :)

[@stawbe]

fyi: you, past exam papers and red wine are my best friends right now. The 4 of us are grinding day and night for my Calc 2 exam next Friday. Thanks so much for all the help!

[@patrickjmt]

Grinding with your friends may help keep up the overall moral but I am not sure if that counts as studying

[@stawbe]

^^ as long as everyone's happy haha

[@thewatcherlollol]

Are you still happy?

[@littlemissmurderer21]

Hope my commenting isn't annoying, but really THANK YOU for making videos! You're saving my college self from crying into my textbook which doesn't explain things or have as great of examples as you do. I hope you feel really happy knowing you're making a difference on a future environmental scientist. I don't know if you still even use this channel, I'd check right now but I'm watching videos and learning, but I hope you see this!!!

[@MuffinTessee]

thanks for helping me get a 4 on my AP Calc AB test!!

[@_MARS_]

THE WAY U MANIPULATED THAT LAST PROBLEM WAS INCREDIBLE AND YET SIMPLE.......U ARE A GENIUS!! CANT SKIP MY LECTURES BCUZ THE GUY GIVES ALOT OF POOP QUIZES.

[@PaIadinKnight]

poop quizzes? xD

[@AdvocareAdster]

I learned how to do this in 3 minutes and 38 seconds thanks to you. Even after going to class and recitation, you explained it better than they ever did. Thank you so much.

[@missjennablejen]

I should just start watching your videos during class when my professor is lecturing. I've learned more in 10 mins than 50 mins from my professor.

[@patrickjmt]

not sure what you mean. they are in order in playlists

[@Cmweinburger]

Patrick, you are a life saver. Your teaching style is great!

[@Ghostoflc]

Ive been trying to figure this out for hours now. It wasn't until i stumbled upon your video that now everything makes so much more sense. You make it clean and easy to understand. THANK YOU!

[@ObsidionDiamond]

You seriously have no idea how much your videos have helped me! You have been the difference maker between me passing and failing calculus! Thanks so much dude! :)

[@alekhile2449]

it's people like you who make it possible for people like me to pass a calc test with a less than stellar professor. thanks again!

[@ActIgnorant]

I owe my math grade to you

[@peyton4048]

+ActIgnorant same brah

[@TheArtunism]

When you see Earl and Doom in one comment chain

[@dumbchicken1]

you mean first born child

[@patrickjmt]

@Minishglob it is the change in x

[@MMAWatch7]

When you got a calc 2 test tomorrow

[@patrickjmt]

+RogueGOW #problemsfrom1/2alifetimeago

[@aaronmason3086]

how did it go!

[@MMAWatch7]

Pretty good, but now I got another one Monday on series and sequence >:[. Hbu?

[@aaronmason3086]

i got a 93 on my first one, second ones on monday , crossing my fingers.. its gonna be harder

[@jhoannajanealberca3642]

hahaha.. 😂

[@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

[@223Warlord]

so du just falls off the map after integrating?

[@kbmagnus12]

+GAO Xiang2 It is just a notation of which variable to integrate. so yes it goes away after integrating

[@shaolin_tcg4727]

thanks I was wondering the same

[@chrisross9467]

kinda like how my dad went to the shops to get some milk but never came back....

[@Really_Biggah]

chris ross I’m so sorry to hear that. Hope u ok

[@thewatcherlollol]

@@chrisross9467 it really do be like that big chungus

[@SnyderChips07]

You're the best Patrick! You've got me through highschool and now you're getting me through college; thanks for the all the work you've put into your videos all these year.

[@maniclokofe4585]

THIS GUY IS THE BEST! I WISH HE COULD BE MY MATH LECTURE

[@harisrg92]

Grade 11 mathematics.. Grade 12 mathematics.. and now finally University Calculus... and I know for sure in future azwell.. you are always going to be there to help me in Math..!! THANK YOU SO MUCH PATRICKJMT!!!!

[@GTiR23]

Thanks man, helped me a lot. You also have the neatest hand writing I've ever seen from a 'lefty'!

[@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 :)

[@manutd931]

YOU SAVED MY BALLS MAN I LOVE YOU.

[@muzicjunky1]

seriously you are a great help. if your not teaching you should write text books. like how to text books with references to your online videos. thank you sooooo very much you are a life saver

[@MrBrandybuck1120]

You, sir, deserve the Presidential Medal of Freedom

[@ak5504]

Dear PatrickJMT, I took Calculus I for Engineers at college without ever previously taking it in high school and I cannot thank you enough, because if it wasn't for you I wouldn't be one of the 3 people in my Calculus I class to have gotten an A, and beating the class average of 45%. Now I am in Calculus II for Engineers and I look forward to using your videos for this semester, and eventually next semester in Calculus III for Engineers! Thank You!

[@afiacco9155]

I am in calc II I just needed a few more of the polynomial. good video your my favorite math teacher. Which is sad lol

[@patrickjmt]

Thanks, that makes me feel good

[@patrickjmt]

Thanks, that makes me feel good

[@noahalexander3607]

I can't even express how thankful I am. My exam isn't till next week but I wouldn't have figured this out if I had not come across your beautiful self.

[@kungaff]

Why do you "tack on" dx on right side when you are derivating both sides at 1:40? Confused :/

[@RockOnDoooooooooood]

You take the derivative of [u=x^2 +4] with respect to x. The real answer you get is du/dx = 2x • dx/dx. The dx/dx gets reduced to 1 and "disappears". Then we want to isolate du so dx is multiplied to both sides. These steps are inferred so that's why you just "tack" on dx on the other side

[@patrickjmt]

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

[@johncarloscorrea]

how do you get u to the 3/4 when you divide u by u to the 1/4?

[@johnnyc4824]

Dividing u by u to the 1/4 gives u to 3/4 because you subtract the powers when dividing. u by itself has power of 1. 1 -- 1/4 = 3/4.

[@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

[@quadhd1121]

I couldn't get how the 2x was delt with in the first example

[@2013Aleksey2013]

+Bley Mamwe He substituted du/2x for dx. ∫2x(u)¹⁰⁰du/2x = ∫(u)¹⁰⁰du

[@FearDBro]

+2013Aleksey2013 im still wondering why though. ok got it so basically he made a new equation that says its equal

[@alekdanser]

+Bley Mamwe that dt=2xdx

[@simply_me7266]

Thank you so much for this video!!! It helped me past my final exam for Calculus 1 last semester!! My professor rushed teaching us how to solve integrals, and i didn't understand a thing!! He then he told us it will be in the finals; and that's when I started to panic!! I'm so glad I came across this video before the finals!! It helped a lot!! Now I'm taking Calculus 2 where we go more in depth with integrals and now we are learning how to use U-substitution. I feel like I'm advanced in the class; its awesome and it's all thanks to you!!

[@david_m157]

They should use his demo's on Mymathlab, who agrees?

[@patrickjmt]

+David M send them a message and let them know

[@david_m157]

Hah, Pearson education may not want good content associated with their name.

[@alanwrigglesworth7562]

our lecturer made it so convoluted i couldn't understand a thing until, once again PatrickJMT became a freaking legend. thank you

[@Horse1083]

You are awesome! Thank god I found you! Keep up the good work! (Even though this is from 2008 lol)

[@auristelabantegui7887]

My first calc exam in Uni is in 36 hours and I'm literally just watching all your videos since I started studying! LMAO you are my saviour thanks!

[@RedBar3D]

I've understood that treating dy/dx as a fraction is a fairly debated and discussed area of mathematics and engineering, even historically. Could someone provide me with an intuitive feel of why treating dy/dx as a fraction is legitimate and why it works? I haven't studied u-substitution or complex differential equations yet, and I wouldn't want to use it without understanding the underlying theory and the underlying proofs. I understand that might be a bit too much to fit into one youtube comment, though. So an intuitive feel for why it works would be great. (alternatively provide me with a link) Thank you :)

[@MorganC-zz1bg]

I believe if you did some research into differentials and infinitesimals you would find your answer.

[@patrickjmt]

multiply top and bottom by 1 - sinx , then use a trig identity on the the denominator, split up the fraction and integrate.

[@sorianobellarmine18]

How many papers have you gone through in your entire career of teaching math through videos?

[@patrickjmt]

beats me. but considering this video has been viewed over 700,000 times, i would wager it is a pretty economical use of paper.

[@sorianobellarmine18]

It is. Thanks for all the videos. You rock.

[@patrickjmt]

thanks nick, you are a stand-up kinda guy

[@Getaneh188]

patrickJMT GREAT job! i don't understand my professor. I just use your videos. you must love maths.

[@dkscidmore]

Video made my day. Been working on this stuff for 4 days now, and these videos explain it so much better than my teacher.

[@noctisvaneixia4276]

what happens to the du?

[@Syndicate6363]

There's a reason your videos always have so many views, thanks man!

[@Wewritestories]

why can't you teach my calc class??????

[@raymondgarcia7223]

Teachers assume students know everything and doesn't teach the obvious. But, you teach also the obvious that's why you became a mentor. Thank you, patrickJMT! :D

[@Darkray99EnMg]

no entiendo ingles pero me gustan tus videos :)

[@patrickjmt]

yo no hablo español , pero me alegro de que te gustan los videos!

[@sophc193]

My calculus teacher made me hate math after a lifetime of loving it, and you reminded me what it's like to love it again. Thank you. :)

[@mrsilvxm]

Have you ever thought about trying to get sponsored by Sharpie ??

[@creampuff966]

I'm pretty sure he is

[@kataals]

You are the best Calculus teacher I know. You make everything so simple and easy to understand. I appreciate you a lot.

[@EngineeringNS]

I love you.

[@EngineeringNS]

This was so confusing! But now I understand how simple it is!

[@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!

[@aedanmcmahon1951]

exam today :(

[@thewatcherlollol]

Howd you do

[@MsToortle]

Calc final tomorrow, teacher doesn't teach. You are my savior. Thank you SO much!

[@alexanderedwards8863]

hes left handed

[@silverzero9524]

yup :(

[@rozikhan2744]

Nah camera is just flipped

[@KillDevilXO]

@@rozikhan2744 lol no it's not....

[@dirtbikedude91]

Good stuff. My teacher is a nice guy, but hardly even explained this... acting like it would just pop into out heads. Turned to KZbin for help and found this video. It's so much clearer what we're trying to do now thanks to you

[@gavin8988898]

Watching these video allows me to skip the lecture! The lecturer took 50mins talking about this and goes nowhere

[@sheenazfazreennuryusof9980]

hey patrickJMT I just wanna give a huge thank you to you! your videos has been a huge help for me. in fact i understand better through watching your video than listening to what the lecturer teach! so thank you and continue doing an amazing job in helping others with calculus! :)

[@kalef1234]

omg get a pop filter haha

[@hammyguybb25]

puh puh puh

[@patrickjmt]

thanks for watching :)

[@dop-a-meme]

That irritating buzzz

[@MultiGoban]

It calms me down, lol. I guess I'm lucky

[@patrickjmt]

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

[@aidanbelleau135]

bbuuuuuzzzzzzzzzzzz

[@LucifertheAtheist]

Patrick, you and khanacademy are probably the best KZbinrs when it comes to maths. Thankyou !!

[@gashmcnash3630]

As long as there is calculus, your videos will be relevant forever.

[@agumonkey]

So envious of people that write calmly and beautifully like you.

[@senzziz]

This guy, help me more when I was in university, now I'm ENGINEER , God bless you

[@999davidstevens]

The best calculus teacher in KZbin!

[@xjoannaxx]

Amazingggg! I'm not even in Calculus and I understand this more than Calculus students do because of you. Thank you so much!

[@purpk86]

Ahhhhhh Patrick! I truly love your videos! Here I am taking second semester calculus and here you are helping me along the way. Thank you so much! You rock!

[@patrickjmt]

it represents the change in x in regards to differentials

[@SekaiiWorld2121]

I had no idea what was going on calculus, but I had a test the next day. Somehow, after watching your videos, I've been able to get a 106 on my test :') you're a magician!

[@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!

[@KlasFerreira]

wow, thank you man! I have tried to understand the substitution technique all week and I didn't understand it when our teacher talked about it. But now after 5 minutes it's easy as hell. THANK YOU!!! :)

[@patrickjmt]

' integrate a rational function of sine and cosine ' is an example i did. not as involved as yours but the same idea.

[@frozenruby23]

I'm taking a first year calculus course and you honestly explained that so much better than my prof.... THANK YOU!

[@etorres61]

Whenever I have a math question, I input the topic in youtube's search bar and I make sure to include patrickJMT next to it. Thanks for the help!

[@patrickjmt]

my pleasure, glad i could help you for so long :)

[@scream4dreams]

i have a good math teacher, but i'd never be able to pass math 140 without you! thanks patrick

[@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!!!!!

[@lthatnemmyguyl1905]

Hey Patrick, recently started studying Engineering and your videos are great! I've gone from being a D- student to a A student in just a semester. Means a lot, and keep it up!!!

[@asinx6665]

dude just know if i pass my exam on monday its all on you sir..great help

[@lanceabagat2605]

Watched your videos right now bcos I need to pass calculus. Thanks, what a lifesaver you are. Two ups!

[@swayamsamal835]

Dude your videos are the best. These are the ones that keeps me going.