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



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

   2
  b  x + a (b - 2 c x)
  -------------------- + 
  c (a + x (b + c x))
   
                   b + 2 c x
    4 a ArcTan[-----------------]
                      2
               Sqrt[-b  + 4 a c]
    -----------------------------
                 2
          Sqrt[-b  + 4 a c]
-(----------------------------------------------------
                        2
                       b  - 4 a c
 
    )

Time to compute: 0.28 second

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