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



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

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

Time to compute: 0.34 second

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