5 ∫             2
   ∘-------cos(x-)--------dx
     cos4(x) + cos2(x ) + 1



optimal
PIC

           (             (      )   )
x + 1 tan−1  ∘--sin(x)cos(x)cos2(x)+1----
3   3          cos4(x)+cos2(x)+1 cos2(x)+1



M 9.01

PIC



Rubi 4.1

PIC



Maple 18

PIC



Sage 5.4

PIC



Fricas 1.2

PIC



sympy 0.7.1

(waited one hr) PIC



Axiom 5/12

PIC



Maxima 5.28.02

PIC



reduce 2008

PIC



mupad 2013a

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



xcas

PIC