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(2*(Cos[x/2] + Sin[x/2])*Sqrt[2 - 2*Sin[x]])/(Cos[x/2] - Sin[x/2])

Integrate[Sqrt[2 - 2*Sin[x]], x] ==
(2*(Cos[x/2] + Sin[x/2])*Sqrt[2 - 2*Sin[x]])/ (Cos[x/2] - Sin[x/2]) 

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

       x        x
2 (Cos[-] + Sin[-]) Sqrt[2 - 2 Sin[x]]
       2        2
--------------------------------------
               x        x
           Cos[-] - Sin[-]
               2        2
Time to compute: 0.07 second
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