oldk1331@gmail.com schrieb:   
   >   
   > > \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.   
      
   Interesting side-effect indeed. It remains to teach FriCAS to insert the   
   necessary dummy operation automatically and silently :). Perhaps the   
   right hand-side of all assignments should simply be evaluated twice   
   before an assignment itself is actually executed.   
      
   PS: The following must not be ignored.   
      
   Where the radical in the former integrand simply has COS(z) and   
   SIN(z)^2, the radical in your synthetic version of the second integrand   
   features SQRT(COS(z)^2) and 1 - COS(z)^2:   
      
     cos(x)/((p*cos(x)+(-1))*(p*(cos(x)^2)^(1/2)+(cos(x)^2+(-1)))^(1/2))   
      
   As generated here by unparse(f::InputForm), your second integrand   
   expectedly does not depend on the presence of the mysterious dummy   
   operation.   
      
   For the integral of exactly this expression:   
      
   \begin{axiom}   
   setSimplifyDenomsFlag(true)   
   integrate(cos(x)/((p*cos(x)+(-1))*(p*(cos(x)^2)^(1/2)+(cos(x)^2+(-1)))   
   ^(1/2)), x)   
   \end{axiom}   
      
   the web interface (FriCAS 1.3.1) also returns:   
      
   >> Error detected within library code:   
      Imaginary part is nonzero. Cannot retract.   
      
   PPS: What is the exact purpose of the FriCAS procedure named rootSimp?   
      
   As tested on the current web interface (FriCAS 1.3.1):   
      
   rootSimp(sqrt(a^2)) ==> a   
   rootSimp(sqrt(a)^2) ==> a   
   rootSimp(sqrt(a^2)-sqrt(a)*sqrt(a)) ==> 0   
      
   rootSimp(sqrt(a*b)) ==> (a*b)^(1/2)   
   rootSimp(sqrt(a)*sqrt(b)) ==> a^(1/2)*b^(1/2)   
   rootSimp(sqrt(a*b)-sqrt(a)*sqrt(b)) ==> a*b)^(1/2)+(-1)*a^(1/2)*b^(1/2)   
      
   Why didn't it "simplify" SQRT(COS(z)^2) in particular?   
      
   Martin.   
      
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