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

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

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

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