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Homework Help: Find the integral. (Note: Solve by the simplest method )

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the integral. (Note: Solve by the simplest method - not all require integration by parts.)
    ∫t ln(t + 2) dt

    2. Relevant equations

    ∫udv=uv-∫vdu

    3. The attempt at a solution

    dv=tdt v=tdt=t2/2
    u=ln(t+2) du=1/(t+2)dt

    ∫t ln(t + 2) dt
    =(t2/2)ln(t+2)-(1/2)∫(t2/2)dt
    =(t2/2)ln(t+2)-(1/2)∫(t-2+(4/(t+2))dt
    =(t2/2)ln(t+2)-(1/2)[(t2/2)-2t+4ln(t+2)]+C
    =? Idk why I keep getting it wrong?
     
  2. jcsd
  3. Feb 14, 2012 #2

    LCKurtz

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    Leave that red part out.
    Check the vdu in that last integral.
     
  4. Feb 14, 2012 #3

    SammyS

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    The above line should be:
    [itex]\displaystyle (t^2/2)\ln(t+2)-(1/2)\int \frac{t^2}{t+2}\,dt\,.[/itex]​
     
  5. Feb 14, 2012 #4
    it reads okay to me, although you missed a step. are you not simplifying enough?
     
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