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(-9*Cos[a*x] + Cos[3*a*x])/(12*a)

Integrate[Sin[a*x]^3, x] ==
(-9*Cos[a*x] + Cos[3*a*x])/(12*a) 

                  3
Integrate[Sin[a x] , x] == 

-9 Cos[a x] + Cos[3 a x]
------------------------
          12 a
Time to compute: < 0.01 second
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