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


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



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

                        2
   2 Tan[a x]   Sec[a x]  Tan[a x]
a (---------- + ------------------)
      3 a              3 a

Time to compute: 0.01 second

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