> \begin{axiom}   
   > setSimplifyDenomsFlag(true)   
   > integrate(cos(z)/((cos(z) - q)*sqrt(cos(z) - q*sin(z)^2)), z)   
   > \end{axiom}   
      
   Trunk version FriCAS proves this integral has no elementary   
   result immediately, with or without setSimplifyDenomsFlag.   
      
   > \begin{axiom}   
   > setSimplifyDenomsFlag(true)   
   > integrate(cos(z)/((p*cos(z) - 1)*sqrt(p*cos(z) - sin(z)^2)), z)   
   > \end{axiom}   
      
   As for this one, trunk version FriCAS doesn't return for a long time,   
   but I accidentally solve it:   
      
   y := 1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2))   
   cos(x)*rootSimp simplify eval(y,x=sin(x))   
   f:=cos(x)*rootSimp simplify eval(y,x=sin(x))   
   integrate(f,x)  -- returns immediately   
      
   Note that the second line does nothing, but without it, integrate   
   won't return immediately.  Strange behavior.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)