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Integration by parts ln(x^2+14x+24)

  1. Mar 14, 2007 #1
    1. The problem statement, all variables and given/known data

    ∫ ln(x^2+14x+24)


    2. Relevant equations

    Integration by parts: ∫ udv = uv - ∫ vdu

    3. The attempt at a solution

    I chose u = ln(x^2+14x+24) and dv = dx therefore

    du = 2x+14/x^2+14x+24 and v = x

    Then once I substitute, I get:

    ∫ ln(x^2+14x+24) = xln(x^2+14x+24) - ∫ (x(2x+14))/x^2+14x+24

    Now I can't figure out how to integrate ∫ (x(2x+14))/x^2+14x+24. I've tried multiplying out, factoring. I thought I might have to use integration by parts again but it's not working out. Any help would be greatly appreciated. Thanks.
     
  2. jcsd
  3. Mar 14, 2007 #2
    Try factoring
    x^2+14x+24=(x+2)(x+12)
    ln(ab)=ln(a)+ln(b)
     
  4. Mar 14, 2007 #3
    for the method you used:

    to integrate the remaining quotient, use long division and then partial fraction.

    *by the way, you should put dx in your integral... some prof. take points off for that.
     
  5. Mar 15, 2007 #4

    Gib Z

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    Homework Helper

    As they should, forgetting your differential is a crime!

    And yes, christianjbs idea is quite easier
     
  6. Mar 15, 2007 #5

    Gib Z

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    Homework Helper

    In fact, if you see ANY quadratic equation inside LN, factor it, even if the solutions are ugly. Makes things much easier.
     
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