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-(Cos[a*x]^(1 + m)/(a + a*m))

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

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

          1 + m
  Cos[a x]
-(-------------)
     a + a m
Time to compute: 0.02 second
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