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(12*c*x + 8*Sin[2*c*x] + Sin[4*c*x])/(32*c)

Integrate[Cos[c*x]^4, x] ==
(12*c*x + 8*Sin[2*c*x] + Sin[4*c*x])/(32*c) 

                  4
Integrate[Cos[c x] , x] == 

12 c x + 8 Sin[2 c x] + Sin[4 c x]
----------------------------------
               32 c
Time to compute: < 0.01 second
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