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(60*b + 60*a*x - 45*Sin[2*(b + a*x)] + 9*Sin[4*(b + a*x)] - Sin[6*(b + a*x)])/(192*a)

Integrate[Sin[b + a*x]^6, x] ==
(60*b + 60*a*x - 45*Sin[2*(b + a*x)] + 9*Sin[4*(b + a*x)] - Sin[6*(b + a*x)])/(192*a) 

                      6
Integrate[Sin[b + a x] , x] == 

(60 b + 60 a x - 45 Sin[2 (b + a x)] + 
 
    9 Sin[4 (b + a x)] - Sin[6 (b + a x)]) / (192 a)
Time to compute: 0.11 second
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