Commercial Macsyma and Mathematica give the same results as you show.
The answers look OK to me.
Raymond Toy wrote:
>Maxima currently says
>
>integrate(x/(1-x^2),x) ->
>-log(1-x^2)/2
>
>and
>
>integrate(x/(x^2-1),x) ->
>log(x^2-1)/2
>
>What does Macsyma (or Mathematica/Maple) say for these integrals?
>
>I think this is the source of the integration bug 1374700.
>
>Ray
>
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