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



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

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

Time to compute: 0.14 second

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