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(13*ArcTan[(-2 + 3*x)/2])/18 + Log[8 - 12*x + 9*x^2]/9

Integrate[(3 + 2*x)/(8 - 12*x + 9*x^2), x] ==
(13*ArcTan[(-2 + 3*x)/2])/18 + Log[8 - 12*x + 9*x^2]/9 

              3 + 2 x
Integrate[---------------, x] == 
                        2
          8 - 12 x + 9 x

          -2 + 3 x
13 ArcTan[--------]                     2
             2        Log[8 - 12 x + 9 x ]
------------------- + --------------------
        18                     9
Time to compute: 0.01 second
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