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Homework Help: Integration by parts question

  1. Feb 20, 2008 #1
    [SOLVED] integration by parts question

    1. The problem statement, all variables and given/known data
    This is part of a larger problem but I'm just not sure if I have the right answer.

    edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex


    2. Relevant equations



    3. The attempt at a solution
    u-substituion:

    [tex]u = x - 7[/tex]

    [tex]du = dx[/tex]

    Integration by parts to get

    [tex]\intlnudu = ulnu - \int1du[/tex]

    [tex] = ulnu - u[/tex]

    [tex] = (x - 7)ln(x - 7) - (y - 7) + C[/tex]

    Now my only problem with this answer is that it gives 7 + C as part of the answer, and I can't recall ever seeing a constant + C as the answer for any integral.

    I actually plugged the equation into this integral finder:

    http://integrals.wolfram.com/index.jsp

    And it told me that it was

    [tex](x-7)ln(x-7) - x[/tex]

    I'm guessing the +C is a given.

    I would just leave it at +C and go on but its part of a differential equation so the value of C ends up being important...
     
    Last edited: Feb 20, 2008
  2. jcsd
  3. Feb 20, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    C is not just a constant in the integration. It's an ARBITRARY constant. There is no difference between C and C+7. Just leave it at C and go on.
     
  4. Feb 20, 2008 #3
    Alright thanks :)
     
  5. Feb 20, 2008 #4
    You mean x-7 and a constant plus a constant is a constant. Both you and mathematica have the right answer, but mathematica just absorbed the 7 into the constant. Differentiate it to check. :)
     
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