I went over some of these using latest Fricas 1.3.5.1 on Linux Manjaro   
      
   On Thursday, October 18, 2018 at 5:24:40 AM UTC-5, clicl...@freenet.de wrote:   
   > This list of 12 noteworthy FriCAS failures collected from my   
   > integration files supersedes its predecessor containing 14 integrals.   
   > A new pseudo-elliptic integrand involving dependent nested roots of   
   > integers has been added at the end:   
   >   
   .....   
   >   
   > - no closed form for Timofeev 5.66 (#401):   
   >   result of integrate(tan(x)/(sqrt(tan(x)) - 1)^2, x) is correct but   
   >   involves symbolic root objects although the defining quartic can be   
   >   factored rationally over the complex numbers.   
   >   
      
   roots still there   
      
   ....   
      
   > - non-elementary Timofeev 8.97.n (#632):   
   >   integrate(log(log(x))^n/x, x) is expressible in functions covered by   
   >   Risch extension, but returned unevaluated, which correctly identifies   
   >   the integral as non-elementary though.   
   >   
      
   Now it returns this   
      
   ii:=integrate(log(log(x))^n/x, x);   
      
       cos(n*pi())*Gamma(n+1,(-1)*log(log(x)))   
      
      
   > - ad-hoc parametrized nested algebraic:   
   >   integrate(1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2)), x)   
   >   fails to return unevaluated.   
   >   
      
   still does not evaluate, gives   
      
   ii:=integrate(1/((p*sqrt(1 - x^2) - 1)*sqrt(p*sqrt(1 - x^2) - x^2)), x);   
   >> Error detected within library code:   
      Denominator not equal to 1   
      
   > - ad-hoc elliptic: integrate((5*x - 9*sqrt(6) + 26)   
   >   /((x^2 - 4*x - 50)*sqrt(x^3 - 30*x - 56)), x) fails to return   
   >   unevaluated.   
   >   
      
   gives   
      
   ii:=integrate((5*x - 9*sqrt(6) + 26)/((x^2 - 4*x - 50)*sqrt(x^3 - 30*x - 56)),   
   x);   
      
      >> Error detected within library code:   
      catdef: division by zero   
      
   ...   
      
   > - infamous cube-root Goursat pseudo-elliptic:   
   >   integrate((1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)), x) fails to   
   >   evaluate.   
   >   
      
   Yes, no response after 20 minutes...terminated.   
      
   > - 4th-root pseudo-elliptic:   
   >   integrate((a + b*x)/((2 - x^2)*(x^2 - 1)^(1/4)), x) fails to evaluate.   
   >   
      
   seems to hang also, waiting about 10 mins.   
      
   > - pseudo-elliptic involving dependent nested roots of integers:   
   >   integrate((7*x + 6*sqrt(17*sqrt(2) + 23) + 9*sqrt(2) + 34)   
   >   /((x + 3*sqrt(2) + 4)*(x + 6*sqrt(sqrt(2) + 1) - 3*sqrt(2) - 2)   
   >   *sqrt(x^3 - 30*x - 56)), x) fails to evaluate.   
   >   
      
   Same result.   
      
      
   > Martin.   
      
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