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Integration by parts

  1. Feb 1, 2010 #1
    the problem is find the integral of xarctan(x^2)dx

    i set w = x^2, so 1/2dw = xdx

    then i plug that into the integral to get

    the integral of 1/2arctan(w)dw

    so i let u = arctan(w) and dv = dw
    so du = dw/(1+w^2) and v = w

    so then the integral of udv = uv - integral of vdu

    so 1/2(w*arctan(w) - integral of w * 1/(1+w^2)dw is what i end up with

    but then if i would have to do integration by parts on the second integral

    which gets me at

    1/2(w*arctan(w) - wln(1+w^2) - integral of ln(1+w^2)dw

    and that gets me stuck due to the having to take the antiderivative of the natural log

    any help would be appreciated. and sorry if its hard to read
  2. jcsd
  3. Feb 2, 2010 #2


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    You can do the second integral using the substitution u=w2+1. You don't need to integrate by parts.
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