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



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

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

Time to compute: 0.24 second

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