6 ∫        ∘ ------------
                  4
  tan (x)  1 + tan (x)dx



optimal
PIC

                       (      2   )
 ∘ ------------   tanh−1 √-1−∘tan4(x)-
12  tan4 (x ) + 1 − -------2√-tan(x)+1--−  12 sinh −1(tan2(x ))
                           2



M 9.01

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Rubi 4.1

PIC



Maple 18

PIC



Sage 5.4

PIC



Fricas 1.2

PIC



sympy 0.7.1

PIC



Axiom 5/12

PIC



Maxima 5.28.02

PIC



reduce 2008

PIC



mupad 2013a

evalin(symengine,'int(tan(x)*sqrt(1+tan(x)^4),x)')  
 
int(tan(x)*(tan(x)^4 + 1)^(1/2), x)



xcas

PIC