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

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

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

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