8 ∫  ∘ ----------------------
         2
     tan  (x ) + 2 tan(x) + 2dx



optimal
PIC

∘ --(----√--)      ( ∘--√--      ∘√----)   ∘ --(√------)        (∘ √----     ∘ --√--)
  12  1 +   5 tan− 1  √1+∘--5tan(x)−---5−1- −    12   5 − 1  tanh −1  √-∘5−1-tan(x)+--1+-5- +  sinh −1(tan(x) + 1)
                      2 tan(x)(tan(x)+2)+2                           2  tan(x)(tan(x)+2)+2



M 9.01

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Rubi 4.1

PIC



Maple 18

image



Sage 5.4

PIC



Fricas 1.2

PIC



sympy 0.7.1

PIC



Axiom 5/12

HTML



Maxima 5.28.02

PIC



reduce 2008

PIC



mupad 2013a

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



xcas

PIC