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


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



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

         x
   2 Sin[-]
         2
---------------
    x        x
Cos[-] - Sin[-]
    2        2

Time to compute: 0.02 second

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