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Homework Help: Need help with integration by parts

  1. Dec 4, 2012 #1
    Hi all this is my first post hopefully i do it right.
    1. The problem statement, all variables and given/known data
    integrate ln^2(6x)dx

    3. The attempt at a solution
    *integral* ln^2(6x)dx
    u=ln^2(6x) dv=dx
    du=(2ln(6x))/x dx v=x

    xln^2(6x)-*integral*x(2ln(6x))/x dx

    xln^2(6x)-2*integral*ln(6x) dx

    u=ln(6x) dv=dx
    du=1/x dx v=x


    MY ANSWER.... that is not correct


    i do not know where i am going wrong and i think im using parts correctly..i dont see any place where substitution could be used but i could be wrong
  2. jcsd
  3. Dec 4, 2012 #2


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    Hah. Well done! I think the only problem is that the -2x should be +2x. You should be able to find where that mistake happened pretty easily.
  4. Dec 4, 2012 #3
    is it because the -2 is distributed and not +2?
  5. Dec 4, 2012 #4


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    If you mean what I think, yes. xln^2(6x)-2(xln(6x)-*integral*dx). (-2)*(-1)=+2.
  6. Dec 4, 2012 #5
    yes! thank you so much.... those simple mistakes will be the death of me!
  7. Dec 5, 2012 #6


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    In your u substitution, have you applied the chain rule correctly?
  8. Dec 5, 2012 #7
    Yes, I believe have.
    Using prime notation:


    since ((6x^1)' = *Const*x^n=*Const*nx^n-1 in my case 6x^1 = 1*6x^1-1
    the 6's cancel and you are left with
    u'=2ln(6x)/x :)
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