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x - (4*Tan[a*x])/(3*a) + (Sec[a*x]^2*Tan[a*x])/(3*a)

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

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

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