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(a*(2 + Sec[x]^2)*Tan[x])/3

Integrate[a*Sec[x]^4, x] ==
(a*(2 + Sec[x]^2)*Tan[x])/3 

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

             2
a (2 + Sec[x] ) Tan[x]
----------------------
          3
Time to compute: < 0.01 second
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