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


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



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

3 x   Sin[2 c x]   Sin[4 c x]
--- + ---------- + ----------
 8       4 c          32 c

Time to compute: < 0.01 second

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