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(35*Sin[a*x])/(64*a) + (7*Sin[3*a*x])/(64*a) + (7*Sin[5*a*x])/(320*a) + Sin[7*a*x]/(448*a)

Integrate[Cos[a*x]^7, x] ==
(35*Sin[a*x])/(64*a) + (7*Sin[3*a*x])/(64*a) + (7*Sin[5*a*x])/(320*a) + Sin[7*a*x]/(448*a) 

                  7
Integrate[Cos[a x] , x] == 

35 Sin[a x]   7 Sin[3 a x]   7 Sin[5 a x]   Sin[7 a x]
----------- + ------------ + ------------ + ----------
   64 a           64 a          320 a         448 a
Time to compute: < 0.01 second
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