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

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

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

            a x        a x
-2 Log[-Cos[---] + Sin[---]] + Log[Sin[a x]]
             2          2
--------------------------------------------
                     a
Time to compute: 0.09 second
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