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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: 0.03 second

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