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


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



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

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

Time to compute: 0.05 second

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