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-2*Sqrt[1 - Cos[x]]*Cot[x/2]

Integrate[Sqrt[1 - Cos[x]], x] ==
-2*Sqrt[1 - Cos[x]]*Cot[x/2] 

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

                        x
-2 Sqrt[1 - Cos[x]] Cot[-]
                        2
Time to compute: 0.01 second
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