Integration using completing the square and the derivative of arctan(x) | Khan Academy

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  • Опубликовано: 15 дек 2024

Комментарии • 49

  • @jdraper12
    @jdraper12 5 лет назад +11

    Great video as always! Although the intermediate with taking the 1/2 out to make the 1/20 coefficient wasn't necessary. I guess this was just to get us familiar with more complex solutions?

  • @issa229
    @issa229 6 лет назад +3

    Beautiful integral! Thanks for the help!

  • @karanveersingh1964
    @karanveersingh1964 3 года назад +1

    Finally i found a video tht helps a lot

  • @vanji7861
    @vanji7861 5 лет назад +3

    wow, thank you for this

  • @jacobramirez598
    @jacobramirez598 4 года назад +1

    Thank you so much!!!

  • @raymondzhao1971
    @raymondzhao1971 5 лет назад +2

    At 4:16, why did he multiply the numerator by 1/2 but then didn't do the same outside the integral? Instead of doing "1/20 x 1/2" outside, he did "1/20 x 2". Im confused....

    • @dhritisuresh8131
      @dhritisuresh8131 5 лет назад +3

      if you substitute dx = 2du, you get 2/(u^2+1), and then you take the 2 out, so its 2/20 integral of 1/ (u^2+1) du, so both ways will get you to the same answer. Hope this helped!

    • @Cynthia_xuefei
      @Cynthia_xuefei 3 года назад

      me too I don't understand

    • @user-tt3vp1uw6o
      @user-tt3vp1uw6o 3 года назад +1

      If you want both sides stay equal you must do what Sal did. Try it yourself. First it was 1 x 1/20 = 1/20. Theo he changed it to 1/2 x 1/10 = 1/20.

  • @samwalker7710
    @samwalker7710 4 года назад

    Thank you for explaining this so well. I found so many videos that skipped steps in the same type of calculation.

  • @tomslawsky4111
    @tomslawsky4111 3 года назад

    Why wouldn't you take the natural log of the denominator?

  • @usernameabcd1915
    @usernameabcd1915 4 года назад +2

    Thank you. This was very helpful. :)

  • @DaAnimalControl
    @DaAnimalControl 3 года назад +1

    why cant you have 5x^-2 -30x^-1, etc. why cant it all just be negative powers?

  • @bonolomasima5192
    @bonolomasima5192 4 года назад

    I love you man. I love your work. God bless you a million.

  • @hunainqazi7576
    @hunainqazi7576 5 лет назад +1

    How can we intregal dx/x2+6×+8

    • @clarrrrk8691
      @clarrrrk8691 5 лет назад

      u do partial fraction
      a/(x+2) + b(x+4)

  • @glennrickelton4093
    @glennrickelton4093 5 лет назад

    Great explanation - clear and precise

  • @drelbey55
    @drelbey55 6 лет назад

    thanks

  • @anmoljangra3047
    @anmoljangra3047 5 лет назад

    Thanks sir

  • @nafisaalhawary9091
    @nafisaalhawary9091 4 года назад +1

    great from egypt

  • @iRReligious
    @iRReligious 6 лет назад

    Wow . that was really nice

  • @saiajynkibito
    @saiajynkibito 5 лет назад +1

    You saved my mind. I was getting closer to a collapse trying to solve a similar question.

  • @tejaspandey993
    @tejaspandey993 5 лет назад +1

    Greaat👌

  • @preyanmehta9275
    @preyanmehta9275 2 года назад

    What happens if there is an X on the top

    • @LuisSanchez-vx9kp
      @LuisSanchez-vx9kp 2 года назад

      You just do regular U-substitution. Letting the trinomial be u. You should then be able to integrate using substitution.

  • @AlexVoxel
    @AlexVoxel 6 лет назад +2

    just a bit complicated huh...

    • @theadel8591
      @theadel8591 5 лет назад

      I bet there’s an easier way but sal presents the complicated ways most of the time

    • @theadel8591
      @theadel8591 5 лет назад

      I solved it without taking 5 and 2^2 out

    • @ijarbis187
      @ijarbis187 5 лет назад

      The Adel that doesn’t change anything lol, taking out the 5 just makes it easier to work with. You only made it harder for yourself also you solved a problem while already knowing the answer which is much easier btw.

    • @shivanshbellamkonda6898
      @shivanshbellamkonda6898 4 года назад

      You can use the formula int(1/(x^2+a^2)=arctan(x/a)

    • @roswelcodiep.bernardo7288
      @roswelcodiep.bernardo7288 2 года назад

      You can actually perform the U-substitution right after you complete the square. No need to factor a 4 on the denominator like the one in the video.

  • @davidsweeney111
    @davidsweeney111 6 лет назад +2

    I love hairy!

  • @EngnrIdris
    @EngnrIdris 6 лет назад +2

    Thanks, that was sweet.
    Can you also please make a video for the integral of sin(6x)cos(3x)dx.

  • @berean22-z8z
    @berean22-z8z 4 года назад

    ........and we are done. Drum row

  • @pomegranate8593
    @pomegranate8593 3 года назад

    you're a rad, mad, thunder attack

  • @allthingsspontaneous491
    @allthingsspontaneous491 4 года назад +18

    I’m going to fail...

  • @roswelcodiep.bernardo7288
    @roswelcodiep.bernardo7288 2 года назад

    You just made things a bit complicated. You can actually proceed on doing the u-substitution after you complete the square, you'll still get the same answer. No more re-engineering.

  • @zakirpasha907
    @zakirpasha907 6 лет назад

    life sava brah

  • @hananilyasa_08
    @hananilyasa_08 Год назад

    di 3:13, bukankah 1/5 diluar integral menjadi 4/5 ,karena kedua sisi dikalikan 1/1/4, tolong bantuannya kawan, agak membingungkan 😔

  • @daahircadeiskacade4038
    @daahircadeiskacade4038 6 лет назад

    Like

  • @uditkumar5747
    @uditkumar5747 6 лет назад

    Thanks