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Homework Help: Integration of a natural log and polynomial

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral when x > 0:

    indefinite integral of ln(x2+19x+84)dx


    2. Relevant equations

    I know I need to use some form of integration by parts: integral of u*dv=uv-(integral of(du*v))

    3. The attempt at a solution

    I began by making u=ln(x2+19x+84) and dv=dx. Thus, (after u-substitution) du=(2x+19)/(x2+19x+84) and v=x.

    After putting that in the formula, we get x*ln(x2+19x+84)-(integral of)((2x2+19x)/(x2+19x+84)). After simplifying that, I get:

    x*ln(x2+19x+84)-((x2+19x+84)(4x+19)-(2x2+19x)(2x+19))/((x2+19x+84)2)

    But according to the program I am using, that is the incorrect answer. Do you have any suggestions? Thanks.
     
    Last edited: Sep 15, 2010
  2. jcsd
  3. Sep 15, 2010 #2
    Why not just factor the quadratic, then split up the integral into two simpler log terms then use:

    [tex]\int ln(u)du=u\ln(u)-u[/tex]
     
  4. Sep 15, 2010 #3
    Hmm, by infinite do you mean definite integral from 0 to infinity? If so, it's clearly divergent.
     
  5. Sep 15, 2010 #4
    No, sorry, I meant the indefinite integral.
     
  6. Sep 15, 2010 #5
    Thanks Jackmell. I tried that method and it worked. (A lot easier than the method I was using.)
     
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