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-Cos[a*x]^2/(2*a)

Integrate[Cos[a*x]*Sin[a*x], x] ==
-Cos[a*x]^2/(2*a) 

Integrate[Cos[a x] Sin[a x], x] == 

         2
-Cos[a x]
----------
   2 a
Time to compute: < 0.01 second
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