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-x + (23*Tan[a*x])/(15*a) - (11*Sec[a*x]^2*Tan[a*x])/(15*a) + (Sec[a*x]^4*Tan[a*x])/(5*a)

Integrate[Tan[a*x]^6, x] ==
-x + (23*Tan[a*x])/(15*a) - (11*Sec[a*x]^2*Tan[a*x])/ (15*a) + (Sec[a*x]^4*Tan[a*x])/(5*a) 

                  6
Integrate[Tan[a x] , x] == 

                              2
     23 Tan[a x]   11 Sec[a x]  Tan[a x]
-x + ----------- - --------------------- + 
        15 a               15 a
 
          4
  Sec[a x]  Tan[a x]
  ------------------
         5 a
Time to compute: 0.02 second
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