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


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



                          2
Integrate[Sqrt[3 - 2 x - x ], x] == 

                        2
(1 + x) Sqrt[3 - 2 x - x ]            1 + x
-------------------------- + 2 ArcSin[-----]
            2                           2

Time to compute: 0.03 second

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