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Integrate[x^3*Tan[x]^4, x] ==
((4*I)/3)*x^3 + x^4/4 - 4*x^2*Log[1 + E^((2*I)*x)] + Log[Cos[x]] + (4*I)*x*PolyLog[2, -E^((2*I)*x)] - 2*PolyLog[3, -E^((2*I)*x)] - (x^2*Sec[x]^2)/2 + x*Tan[x] - (4*x^3*Tan[x])/3 + (x^3*Sec[x]^2*Tan[x])/3

           3       4
Integrate[x  Tan[x] , x] == 

          4
4 I  3   x       2          (2 I) x
--- x  + -- - 4 x  Log[1 + E       ] + Log[Cos[x]] + 
 3       4
 
                       (2 I) x
  (4 I) x PolyLog[2, -E       ] - 
 
                             2       2
                 (2 I) x    x  Sec[x]
  2 PolyLog[3, -E       ] - ---------- + x Tan[x] - 
                                2
 
     3           3       2
  4 x  Tan[x]   x  Sec[x]  Tan[x]
  ----------- + -----------------
       3                3