U-Substitution - More Complicated Examples

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  • čas přidán 4. 04. 2008
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Practice Problems with Solutions made by me!:
    Basic U-Substitution Examples • ❖ Integration using U-...
    U-Substitution - More Complicated Examples - Using U-substitution to find antiderivates. These examples are slightly more complicated than the examples in my other video!

Komentáře • 592

  • @tms1266
    @tms1266 Před 2 lety +37

    Excellent explanation.
    There was a little mistake. For the third problem, the denominator has + between (1-x^2) and sqrt(1-x^2). That being said, you would need change the minus sign in your denominator between u and square root of you, v^2 and v, and finally between square root of (1-x^2) and 1 at the ending result.

  • @MrTom510513
    @MrTom510513 Před 10 lety +165

    u made a mistake on 4:37- 4:41. It should be a "+" sign

    • @Nithesh2002
      @Nithesh2002 Před 7 lety +6

      chan tom thanks, I thought I messed up hahah

    • @mannyramirez8265
      @mannyramirez8265 Před 6 lety +1

      Nithesh S. he factored out a negative, thus changing the inside functions polarity

    • @gaurav.raj.mishra
      @gaurav.raj.mishra Před 6 lety +18

      Manny Ramirez Nope

    • @mikekato7761
      @mikekato7761 Před 6 lety +5

      Sure he messed up

    • @henryjiang9664
      @henryjiang9664 Před 6 lety +8

      Mike Kato The solution should be -ln|sqrt(1-x^2)+1|) + c

  • @fluffybasket5674
    @fluffybasket5674 Před 9 lety +272

    Can you please replace my calculus professor?

    • @agilasadi5044
      @agilasadi5044 Před 5 lety

      mine too

    • @Corentinbes
      @Corentinbes Před 5 lety +10

      Calculus professor substitution

    • @MG-hi9sh
      @MG-hi9sh Před 5 lety

      Mac Just watch his videos instead man. Bin your professor.

    • @Infinitesap
      @Infinitesap Před 4 lety +1

      Don't you mean SUBSTITUTE? :)

  • @tncreations1267
    @tncreations1267 Před 6 měsíci +4

    Just letting you know that your video is still helping people to get through calculus. Thank you very much.

  • @thatguyoverthere54
    @thatguyoverthere54 Před 9 lety +48

    7 years later, and this video still helps Calculus students like me :)

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @bobish101 so for x in your u = 16 + 2x part; then plug that in, divide it out and integrate

  • @acoti
    @acoti Před 14 lety +1

    I never would have thought to do a double substitution. Your work is amazing and I've been watching your Integration videos for a few days now and they're helping me so much! Thank you for these videos.

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @bamf703 trying to keep the v's from lookin' like u's

  • @jonnyd6087
    @jonnyd6087 Před rokem

    I love your little comments catering to the people LEARNING. One of my biggest problems with some professors is they seem to not address or display any understanding or acknowledging the difficulty something might have for people who are LEARNING. Your comments show you are a very good teacher by acknowledging that "when you don't know how to do something, sometimes it seems like the hardest thing ever".

  • @AfroQueenB
    @AfroQueenB Před 13 lety +1

    at the beginning of the day i couldn't be able to explain what U-substitution even had to do with anything but after watching all of patricks U-Substitution videos I've learned more than my teacher or my stupid calc book could ever teach me. Kudos from MA.

  • @chococookies1435
    @chococookies1435 Před 10 lety +3

    Sometimes I feel like you are a magical mystical being that just KNOWS.
    Thanks for being awesome!

  • @patrickjmt
    @patrickjmt  Před 15 lety +2

    the first integral can not be integrated.
    you would use a series expansion to approximate it to any desired amount of accuracy however.
    the second integral is just arctan(x).
    for the third, i assume you mean:
    1/[x(4x+1)^1/2]
    at a glance like you would let u = (4x+1)^1/2
    solve for x, find dx, plug it all in and you would have a problem that you would have to use partial fractions on

  • @zahranaseri4759
    @zahranaseri4759 Před 9 lety +3

    Many Thanxx, you're my hero. I don't know why my lecturer couldn't teach it as clear as you.

  • @seizureboy999
    @seizureboy999 Před 9 lety +139

    your v's look like square roots :(

  • @CHAPPYx12
    @CHAPPYx12 Před 12 lety +1

    Thank you soo much for these videos. My teacher shows us the easiest example and then expects us to learn the rest on our own, you pretty much are my Calculus teacher, thanks, you rock!

  • @colliefarm570
    @colliefarm570 Před 2 lety +1

    Once again, thank you for these videos which are concise, explain the theory AND how to do it (the algebra part). My calc I teacher does his best to explain these things but it doesnt make sense. I've been using your videos since last summer's Trig class with him and now for Calc I (my husband used your videos as well when he was in school and is the one who suggested you). What a BLESSING! Your videos are the main reason Im grasping the concepts and how to do the problems. And with finals coming up in 8 days, theyre helping me learn and review everything as well! See ya in Calc II. thanks again!

  • @lailamahmudah5217
    @lailamahmudah5217 Před 6 lety

    10 years later and I still find this video useful. Thank you Sensei

  • @patrickjmt
    @patrickjmt  Před 15 lety

    whats wrong with natural log? : )

  • @bluestaragar3976
    @bluestaragar3976 Před 7 lety +1

    Night before Calc BC test feeling pretty great about it. This video reinforced my confidence. Thnx bro

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @AhOhy sorry, i do not do hw questions - it could be stuff for a grade and i am not comfortable answering that. however, i will give you a hint: you picked the wrong u sub.

  • @Team3DAlpha
    @Team3DAlpha Před 12 lety

    QUESTION around 05:08 i still don't understand why you had to square the square root of U. I'm confused as to why we can't write it as U to the one half and then differentiate. Sorry i haven't done calc in a while and i'm rusty as *$%^.

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @cincottallll so teach yourself if you are that interested in it! why wait for someone to 'teach' you? although you need some trig as well before you jump into it.

  • @haruharu380
    @haruharu380 Před 4 lety

    12 years and counting but bruh u're still helping a lot of students who are unfortunate on math teachers sskksks hope you're earning what's right for you now.

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @mylesbianify well i assume you meant u-substitution. if he meant trig substitution, that is correct

  • @patrickjmt
    @patrickjmt  Před 16 lety +2

    yes! you are absolutely correct! it should be u + u^5! thanks for pointing out the error!

  • @CodyBalos
    @CodyBalos Před 8 lety +12

    It'd be pretty cool if in videos where all you are doing is examples, you showed a preview of each type of problem you will do with links to the time that you do each example. It might not be worth the effort, but just a thought! Thanks for all your videos, they have helped me go from a B math student to 94% in Calc I!

    • @patrickjmt
      @patrickjmt  Před 8 lety +7

      +Cody Balos that is a good idea, i will keep this in mind for future videos

  • @patrickjmt
    @patrickjmt  Před 13 lety +1

    @vhskeva ha! glad you like the videos so much : ) sometimes i turn on like 15 videos at once and get a surreal patrickjmt effect. my wife thinks i am crazy ( i also do it to annoy her!!)

  • @shintaayam
    @shintaayam Před 8 lety +4

    How could i just found your channel!!?? You teach so good, better than my math teacher

  • @hanamcavoy6952
    @hanamcavoy6952 Před 6 lety

    Finally understood this before 2 hours from the exam! Subscription well deserved sir

  • @habooshirahhal2581
    @habooshirahhal2581 Před 9 lety +1

    Thank u soooo much for your videos!! You're such a great teacher I always recommend ur videos to my friends 😊 I really find them very useful and they have helped me a lot!! Thank u again!

  • @patrickjmt
    @patrickjmt  Před 15 lety

    well, you can treat it as a fraction!
    plus, we are calculating the differential:
    the differential of u = e^x
    is du = e^x dx

  • @neodine
    @neodine Před 12 lety +1

    You and Sal really helped to pass all my uni math courses, big thanks to you!

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @sam1209 sometimes it is nice to take the scenic route.

  • @radaradaitsbob
    @radaradaitsbob Před 11 lety

    You teach way better than my teacher! Finally, something I can understand. Now I can ace the test I have tomorrow. :) Thank you for all your hard work~

  • @zzypingan
    @zzypingan Před 15 lety

    great video very clear! just to mention that to others who is watching this video, the question involving 2 substitutions does not necesserily need 2 subs, u^2=1-x^2 gives same answer.

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @JRaby21 u have to use taylor series. it does not have an elementary antiderivative

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @mylesbianify no, you can not. it looks like a trigonometric substitution to me (after completing the square)

  • @odinheim
    @odinheim Před 14 lety

    Patrick we all thank you so much you made our math's struggle an easy task , without you we have not passed our exams
    thanks
    we should make a donation to support you for what you do without any financial interests
    we all love you
    long live the mathematics and the mathematicians

  • @MrJrred299
    @MrJrred299 Před 8 lety +1

    Great explanation...very comprehensive examples...Thanks

  • @GenaEnSamIAm
    @GenaEnSamIAm Před 7 měsíci

    Today I am a what I'd like to call a successful engineer.
    Thank you Patrick.
    We all owe you.

  • @john121447
    @john121447 Před 11 lety

    you have perfect handwritting , explanation skills as well as pace

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @omegaplatypus cause i used to get them cofused with ' u ' so i put a little hook on them to help myself

  • @JasonRobards2
    @JasonRobards2 Před 11 lety

    Thanks Patrick, this video helped a lot. The problem at min 8 was just the one I was stuck at.

  • @Phalanx73
    @Phalanx73 Před 13 lety

    Thanks a lot:I have an exam tomorrow, I was absent when my class was doing substtitution techniques, I got a handout my teacher made on it so I can study but it was like bullshit...so, there I was looking for help on the internet, and found just the one! It was easy to understand I didnt need to re-watch it many times to grab the idea of it...too bad YOU arent my teacher!!!lol pls keep uploading!! thx.

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @ladyasphodel i prefer complicating things as much as possible.

  • @ultimatekenz
    @ultimatekenz Před rokem

    14 years ago! thank you for posting this!

  • @KhaozOfTrouble18
    @KhaozOfTrouble18 Před 12 lety

    I have a test about this today. This just made me understand everything! Thanks

  • @MARTINREN1231
    @MARTINREN1231 Před 9 lety +1

    this helped me in so many ways O: thank youuuuuuu(because what they discussed in school is far away from what is given to us in assignments and exams xD)

  • @BYMYSYD
    @BYMYSYD Před 13 lety

    This was very helpful. Thanks Patrick.

  • @TheUSASecret
    @TheUSASecret Před 8 lety +25

    I want you pens ... that is why people are good at math, sometimes they want to write with cool pen.

  • @ganendrav
    @ganendrav Před 8 lety +26

    hi patrick, at 4:46 u wrote u - sqrt(u) . it should be +
    small error but great video nonetheless. thank you!

  • @bmwbaby90
    @bmwbaby90 Před 12 lety

    i love u patrick because of u i passed my calculus classes

  • @christianpatrickfernandez62

    AWESOME VIDEO. You sir just saved me from alot of trouble. 👏🏻

  • @alhaithamaljabri2203
    @alhaithamaljabri2203 Před 6 lety

    2017 and you rock all the time!

  • @akksay
    @akksay Před 8 lety

    You are the best mathematician I have ever known!

  • @edel1561
    @edel1561 Před 12 lety +2

    OMG you are actually amazing! you are helping me with so much of my university work! i love you" you are a genius! and such a good teach! you explain things so well! :)

  • @jackrutledgegoembel5896

    Fantastic explanations!

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @D4ntesword yes, that is wht i would do

  • @adanuokoko5414
    @adanuokoko5414 Před 9 lety +1

    thank you so much. your video has been so helpful

  • @patrickjmt
    @patrickjmt  Před 16 lety

    yes, sorry about that! someone else pointed it out! i add text comments into the video so that people will now be aware of the mistake. Thanks for pointing it out!!!

  • @ftwi49
    @ftwi49 Před 13 lety

    omg u saved my life!! my high school calc teacher is terrible and because of that my grade is falling, but with your video you totally saved my ass! thank you!!!

  • @patrickjmt
    @patrickjmt  Před 16 lety

    great! glad it helped

  • @davidrollins9229
    @davidrollins9229 Před 8 lety +3

    For the last problem you can just set u to x+4 instead of (x+4)^(1/3)
    U=x+4
    X=u-4
    Du=dx
    Integrate (u-4)*u^(1/3) du
    To get the same answer... But a little simpler

  • @ommyskills8799
    @ommyskills8799 Před 7 lety +1

    the best lecturer ever..now I like calcus coz of u.

  • @b5thomas7
    @b5thomas7 Před 14 lety

    I really appreciate your vids - very helpful

  • @numa1401
    @numa1401 Před 8 lety +1

    Good examples with better explanation, get it boy......Thanks for the video..

  • @mafiaSage105
    @mafiaSage105 Před 11 lety

    You. Patrick. GENIUS !!!!

  • @theson22788
    @theson22788 Před 7 lety +12

    i find the hardest thing to do is double or triple substitution.i lost track of them quite a bit.

  • @Jezebel1115
    @Jezebel1115 Před 7 lety +1

    Great video very helpful. Thanks!!!

  • @chadwad12
    @chadwad12 Před 12 lety

    I used to think this kind of math was just dumb to do. Then I found Patrick. Anytime I have a question about how to do something I immediately search your website and CZcams Channel. It immediately becomes clearer and a light bulb pops into my head. Now I almost look forward to moving into my higher level math classes at my university as I work towards my Computer Science degree.

  • @b19fell
    @b19fell Před 15 lety

    Cheers, these are great tutorials!!!

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @TrAnScEnD3nT derivative of e^x is e^x

  • @TheMvrocks
    @TheMvrocks Před 14 lety

    love studing this way man thanks a lot

  • @rockstar377
    @rockstar377 Před 10 lety +1

    I'm failing my math class because my teacher can't explain how to do anything but you are saving me right now I think I will pass. Haha. thank you.

  • @daweriqbal7216
    @daweriqbal7216 Před 5 lety +1

    2k19 and tomarrow is my calculus exam... THANKS BOI👍

  • @Actraiser1
    @Actraiser1 Před 8 lety +115

    That third example is satanic. Would never get that on a test :/

    • @ruskodudesko9679
      @ruskodudesko9679 Před 7 lety +3

      Average? That's like you have to be able to do it in your head in my course - try ⌡√(tanx)dx

    • @rajatbansal512
      @rajatbansal512 Před 7 lety

      What course are you talking +rusko dudesko

    • @ruskodudesko9679
      @ruskodudesko9679 Před 7 lety +1

      Rajat Bansal calc 2

    • @rajatbansal512
      @rajatbansal512 Před 7 lety

      *****​ k which university or college

    • @ruskodudesko9679
      @ruskodudesko9679 Před 7 lety

      Rajat Bansal at a community college - I'm transferring to UCSC as a junior, here is a question I pulled from random on an exam:
      ⌡1/(2-sinx)dx
      and one I picked just to prove this guy wrong:
      ⌡(2x+1)/(x^4+x)dx

  • @FlippinPin0y
    @FlippinPin0y Před 15 lety

    The way you explain it is so clear and is can be easily understood, and the way you film it particularly helps too. Are you sniffing the marker? lol jk, thank you very much!

  • @laurauribe3445
    @laurauribe3445 Před 10 lety +2

    You're simply amazing.

  • @magnusrobinson8735
    @magnusrobinson8735 Před 8 lety +2

    Hi Patrick, Regarding the third question. Why did you choose such a difficult U substitution? I used U=x+4 and it's much easier to follow. I don't mind the U sub used mainly because it showed me a different way of doing it but I found that more difficult. I'm just saying in case someone was thinking of doing the same I did. Thanks for all the help. You're pretty much a super hero to me!

    • @kyleairforce
      @kyleairforce Před 8 lety

      I did it the same way and got the same answer.

  • @patrickjmt
    @patrickjmt  Před 13 lety

    @cdromurmom no.

  • @MsAgnosia
    @MsAgnosia Před 8 lety +2

    I usually have difficulty in figuring out whether to do substitution before integration by parts or after, is there any way that can help me understand it better? Also, thanks for all the videos, they are a life saver :) !

  • @AliMohammadRahimi
    @AliMohammadRahimi Před 11 lety

    Hello, i want to thank you, you are doing very very good job that helped me to know more integration in Deferential Equation, thanks allot.

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @TheRoadofDestruction i do not have a time limit any more : )

  • @charlesdrew7330
    @charlesdrew7330 Před 12 lety

    Wohaaaw I love the feeling of achieving correct solutions... LOVE YOU

  • @chucksneedmoreland
    @chucksneedmoreland Před 14 lety

    Everyone should stop complimenting patrick's teaching style, because then he might go and teach again.
    This dark prospect must not, cannot, will not happen! What would we do then?!?
    j/k
    Thanks for the help. Finally I get u-substitution.

  • @megaelliott
    @megaelliott Před 15 lety

    i see by your wide range of the english vocabulary, that you would do even better in an english exam

  • @marcushines4172
    @marcushines4172 Před 8 lety +6

    You are a F'ing legend bro!

  • @14jlim
    @14jlim Před 14 lety

    ive been watching your videos, and you should be duplicated and be shared to all universities in the world, to make our lives easier. thanks by the way for your videos

  • @SibirianBlue
    @SibirianBlue Před 13 lety

    Excellent! Thank you from England :)

  • @patrickjmt
    @patrickjmt  Před 12 lety

    @motheahmad29 politics in usa is an amazingly wacky, ineffective mess. the last thing i would want to do is get involved in it. i would go back to waiting tables before i would be president.

  • @Mitchman240
    @Mitchman240 Před 13 lety

    This was great, thanks....mate.

  • @patrickjmt
    @patrickjmt  Před 16 lety

    yep! you are right

  • @Tsusuu1
    @Tsusuu1 Před 15 lety

    Wow these are awesome!!! :D Thanks!!

  • @danelnugmanova4007
    @danelnugmanova4007 Před 9 lety +1

    perfect explanations!!!!

  • @mehedihasanmahi9134
    @mehedihasanmahi9134 Před rokem

    MR Patrick we need more videos what are your thoughts on organizing a an integration maths competition

  • @patrickjmt
    @patrickjmt  Před 15 lety

    no problem!

  • @gluiz90
    @gluiz90 Před 14 lety

    Great Video! Extremely helpful. Wish you could be my calc teacher.

  • @kennys3095
    @kennys3095 Před 11 lety

    Great Videos Patrick!
    But can you please tell me how do we get to know about when to use the U-Sub?

  • @indigohnoes
    @indigohnoes Před 11 lety

    SUPEr helpful. Thank you so much

  • @todopic
    @todopic Před 15 lety

    Simplemente impresionante!!
    Thanks teacher is great!!!!