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


Integrate[1/(a + b*x + c*x^2), x] ==
(2*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/ Sqrt[-b^2 + 4*a*c]



                1
Integrate[--------------, x] == 
                       2
          a + b x + c x

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

Time to compute: 0.02 second

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