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Integrate[(a + b*x + c*x^2)^(-3), x] ==
(-(((b + 2*c*x)*(b^2 - 6*b*c*x - 2*c*(5*a + 3*c*x^2)))/(a + x*(b + c*x))^2) + (24*c^2*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/ Sqrt[-b^2 + 4*a*c])/(2*(b^2 - 4*a*c)^2)



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

                 2                             2
   (b + 2 c x) (b  - 6 b c x - 2 c (5 a + 3 c x ))
(-(-----------------------------------------------) + 
                                  2
                 (a + x (b + c x))
 
        2            b + 2 c x
    24 c  ArcTan[-----------------]
                        2
                 Sqrt[-b  + 4 a c]
    -------------------------------) / 
                  2
           Sqrt[-b  + 4 a c]
 
       2         2
  (2 (b  - 4 a c) )

Time to compute: 0.29 second

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