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Integrate[x/((-1 + x)^2*(2 + x)^2), x] ==
((3*(-4 + x))/(-2 + x + x^2) + Log[2 - 2*x] - Log[2*(2 + x)])/27

                  x
Integrate[------------------, x] == 
                  2        2
          (-1 + x)  (2 + x)

3 (-4 + x)
----------- + Log[2 - 2 x] - Log[2 (2 + x)]
          2
-2 + x + x
-------------------------------------------
                    27