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Integrate[x/(1 + Sqrt[b + a*x]), x] ==
-(x/a) + ((-2*(-3 + 2*b))/(3*a^2) + (2*x)/(3*a))* Sqrt[b + a*x] - (2*(1 - b)*ArcTanh[Sqrt[b + a*x]])/ a^2 + ((-1 + b)*Log[-1 + b + a*x])/a^2



                  x
Integrate[-----------------, x] == 
          1 + Sqrt[b + a x]

  x     -2 (-3 + 2 b)   2 x
-(-) + (------------- + ---) Sqrt[b + a x] - 
  a            2        3 a
            3 a
 
  2 (1 - b) ArcTanh[Sqrt[b + a x]]
  -------------------------------- + 
                  2
                 a
 
  (-1 + b) Log[-1 + b + a x]
  --------------------------
               2
              a

Time to compute: 0.12 second

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