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-ArcTan[(-2 + 3*x)/Sqrt[5]]/(3*Sqrt[5]) + Log[3 - 4*x + 3*x^2]/6

Integrate[(-1 + x)/(3 - 4*x + 3*x^2), x] ==
-ArcTan[(-2 + 3*x)/Sqrt[5]]/(3*Sqrt[5]) + Log[3 - 4*x + 3*x^2]/6 

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

        -2 + 3 x
-ArcTan[--------]                    2
        Sqrt[5]     Log[3 - 4 x + 3 x ]
----------------- + -------------------
    3 Sqrt[5]                6
Time to compute: 0.03 second
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