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(5*x)/16 - (15*Sin[2*a*x])/(64*a) + (3*Sin[4*a*x])/(64*a) - Sin[6*a*x]/(192*a)

Integrate[Sin[a*x]^6, x] ==
(5*x)/16 - (15*Sin[2*a*x])/(64*a) + (3*Sin[4*a*x])/(64*a) - Sin[6*a*x]/(192*a) 

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

5 x   15 Sin[2 a x]   3 Sin[4 a x]   Sin[6 a x]
--- - ------------- + ------------ - ----------
16        64 a            64 a         192 a
Time to compute: < 0.01 second
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