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


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



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

        1 + m
Sin[a x]
-------------
   a + a m

Time to compute: 0.02 second

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