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(2*(-Log[2*Cos[x/4]] + Log[2*Sin[x/4]])*Sin[x/2])/Sqrt[1 - Cos[x]]

Integrate[1/Sqrt[1 - Cos[x]], x] ==
(2*(-Log[2*Cos[x/4]] + Log[2*Sin[x/4]])*Sin[x/2])/ Sqrt[1 - Cos[x]] 

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

              x               x        x
2 (-Log[2 Cos[-]] + Log[2 Sin[-]]) Sin[-]
              4               4        2
-----------------------------------------
            Sqrt[1 - Cos[x]]
Time to compute: 0.04 second
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