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

                    3    4
          -1 - x - x  + x
Integrate[----------------, x] == 
                2    3
              -x  + x

        2
  1    x
-(-) + -- - 2 Log[-1 + x] + 2 Log[x]
  x    2