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(a + a*Cot[a*x])^(-1)

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

                               -2
Integrate[(Cos[a x] + Sin[a x])  , x] == 

      1
--------------
a + a Cot[a x]
Time to compute: 0.03 second
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