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(-2*Sqrt[3]*(a - b)*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*(a + b)*Log[-1 + x] - (a + b)*Log[1 + x + x^2] + 2*c*Log[-1 + x^3])/6


Integrate[(a + b*x + c*x^2)/(-1 + x^3), x] ==
(-2*Sqrt[3]*(a - b)*ArcTan[(1 + 2*x)/Sqrt[3]] + 2*(a + b)*Log[-1 + x] - (a + b)*Log[1 + x + x^2] + 2*c*Log[-1 + x^3])/6



                       2
          a + b x + c x
Integrate[--------------, x] == 
                   3
             -1 + x

                           1 + 2 x
(-2 Sqrt[3] (a - b) ArcTan[-------] + 
                           Sqrt[3]
 
                                                 2
    2 (a + b) Log[-1 + x] - (a + b) Log[1 + x + x ] + 
 
                  3
    2 c Log[-1 + x ]) / 6

Time to compute: 0.08 second

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