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Integrate[(5 + 3*x)/(1 - x - x^2 + x^3), x] ==
-4/(-1 + x) - Log[-1 + x]/2 + Log[1 + x]/2

              5 + 3 x
Integrate[---------------, x] == 
                   2    3
          1 - x - x  + x

  -4     Log[-1 + x]   Log[1 + x]
------ - ----------- + ----------
-1 + x        2            2