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-((a*x + Cot[a*x])/a)

Integrate[Cot[a*x]^2, x] ==
-((a*x + Cot[a*x])/a) 

                  2
Integrate[Cot[a x] , x] == 

  a x + Cot[a x]
-(--------------)
        a
Time to compute: < 0.01 second
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