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Integration by Parts

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data
    Find or evaluate the integral using substitution first, then using integration by parts.

    [tex]\int \ln (x^2 + 1) \, dx [/tex]

    3. The attempt at a solution

    [tex]Let \: u = x^2 + 1[/tex]

    [tex]du = 2x \, dx[/tex]

    [tex]dx = \pm \frac{du}{2 \sqrt{u - 1}}[/tex]


    [tex]\int \ln (x^2 + 1) \, dx = \pm \frac{1}{2} \int \frac{\ln u}{\sqrt{u-1}}\, du[/tex]

    I don't know where to go from here. I tried to integrate by parts and it just turned into a mess. Am I approaching this the wrong way?
  2. jcsd
  3. Jan 28, 2010 #2


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    I'm not sure what substitution they think you ought to make. It's pretty easy if you apply parts right off regarding the original integral as u*dv where u=ln(1+x^2) and v=x.
  4. Jan 28, 2010 #3
    Got it. Thanks.
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