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(2*(Cos[x/2] + Sin[x/2])*Sqrt[1 - Sin[x]])/(Cos[x/2] - Sin[x/2])

Integrate[Sqrt[1 - Sin[x]], x] ==
(2*(Cos[x/2] + Sin[x/2])*Sqrt[1 - Sin[x]])/ (Cos[x/2] - Sin[x/2]) 

Integrate[Sqrt[1 - Sin[x]], x] == 

       x        x
2 (Cos[-] + Sin[-]) Sqrt[1 - Sin[x]]
       2        2
------------------------------------
              x        x
          Cos[-] - Sin[-]
              2        2
Time to compute: 0.04 second
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