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

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

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

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