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(-3*Cos[a + b*x])/(4*b) + Cos[3*(a + b*x)]/(12*b)

Integrate[Sin[a + b*x]^3, x] ==
(-3*Cos[a + b*x])/(4*b) + Cos[3*(a + b*x)]/(12*b) 

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

-3 Cos[a + b x]   Cos[3 (a + b x)]
--------------- + ----------------
      4 b               12 b
Time to compute: 0.01 second
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