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Integrate[(3*x - 4*x^2 + 3*x^3)/(1 + x^2), x] ==
(x*(-8 + 3*x))/2 + 4*ArcTan[x]

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

x (-8 + 3 x)
------------ + 4 ArcTan[x]
     2