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


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



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

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

Time to compute: 0.11 second

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