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

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

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

                                2
   2 Tan[b + a x]   Sec[b + a x]  Tan[b + a x]
a (-------------- + --------------------------)
        3 a                    3 a
Time to compute: 0.02 second
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