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(2*(a + Sqrt[x])^(1 + b)*(-a + (1 + b)*Sqrt[x]))/(2 + 3*b + b^2)

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

                       b
Integrate[(a + Sqrt[x]) , x] == 

               1 + b
2 (a + Sqrt[x])      (-a + (1 + b) Sqrt[x])
-------------------------------------------
                          2
               2 + 3 b + b
Time to compute: 0.03 second
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