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Intergration by Parts (IbP) problem

  1. Feb 12, 2008 #1
    [tex]\int_{1} ^{2e} x^2(ln x)^{2} dx[/tex]

    I need to solve this using IbP. I made the following:

    [tex]u = (ln x)^2[/tex]

    [tex]du = (\frac{2 ln x}{x}) dx[/tex]

    [tex]dv = x^2 dx[/tex]

    [tex]v = \frac{x^3}{3}[/tex]

    So I get:
    [tex](ln x)^2 (\frac{x^3}{3}) \|_{1} ^{2e}[/tex][tex]- \int_{1} ^{2e} (\frac{x^3}{3}) 2 ln x dx[/tex]
    (not sure how to make this look right)

    Is this right?
    Where do I go from here? Thanks
  2. jcsd
  3. Feb 12, 2008 #2
    Integrate by parts again.
  4. Feb 13, 2008 #3
    So what I have is right so far? I just IbP on the RHS?
  5. Feb 13, 2008 #4
    Yup, if you've integrated ln(x) before, it should be obvious that you can integrate it again.
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