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Integrate[Sqrt[a + b*x + c*x^2]/x, x] ==
Sqrt[a + x*(b + c*x)] + Sqrt[a]*Log[a^(3/2)*x] - Sqrt[a]*Log[2*a + b*x + 2*Sqrt[a]* Sqrt[a + x*(b + c*x)]] + (b*Log[b + 2*c*x + 2*Sqrt[c]*Sqrt[a + x*(b + c*x)]])/ (2*Sqrt[c])

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

                                     3/2
Sqrt[a + x (b + c x)] + Sqrt[a] Log[a    x] - 
 
  Sqrt[a] Log[2 a + b x + 
 
     2 Sqrt[a] Sqrt[a + x (b + c x)]] + 
 
  b Log[b + 2 c x + 2 Sqrt[c] Sqrt[a + x (b + c x)]]
  --------------------------------------------------
                      2 Sqrt[c]