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


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



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

                      2              b x
                     a  ArcTan[----------------]
        2    2  2                    2    2  2
x Sqrt[a  - b  x ]             Sqrt[a  - b  x ]
------------------ + ---------------------------
        2                        2 b

Time to compute: 0.04 second

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