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Integration By Parts(stuck on one part)

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate the Definite Integral
    Integral[0,1] Ln(x^2+1) dx

    2. Relevant equations



    3. The attempt at a solution
    So far I have done the first part,
    U= Ln (x^2+1) Du= 2x/(x^2+1)dx
    Dv= 1 dx V=x

    x* Ln(x^2+1)- Integral [0,1] (2x^2/(x^2+1) dx

    But I'm stuck on the second integral, I have tried punching into a TI-89, but It comes out to a weird answer. Can someone help?
     
  2. jcsd
  3. Feb 15, 2009 #2

    Dick

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    Start by dividing the polynomial x^2+1 into x^2 to express it as quotient and remainder.
     
  4. Feb 15, 2009 #3
    What do I do after that? How does that help?
     
  5. Feb 15, 2009 #4

    Dick

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    x^2/(1+x^2)=1-1/(1+x^2). You can integrate 1 and you should be able to integrate 1/(1+x^2). It's an inverse trig function.
     
  6. Feb 15, 2009 #5
    Oh wow, thanks!
    :smile:
     
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