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


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



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

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

Time to compute: 0.05 second

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