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


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



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

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

Time to compute: 0.17 second

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