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


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



               1
Integrate[------------, x] == 
          1 + Tan[a x]

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

Time to compute: 0.04 second

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