oldk1331@gmail.com schrieb:   
   >   
   > Here's some comments (not  excuses!) on the "failed 14 Timofeev   
   > problems":   
   >   
   >  (-2*cos(x)^3*(-1+sin(x))+cos(2*x)*sin(x))/(sin(x)^2*sqrt(-5+sin(x)^2))   
   >   
   > This integrand is not real, because of the 'sqrt(-5+sin(x)^2)' part.   
   >  In FriCAS, 'complexIntegrate' can give a result.  If replace   
   > 'sqrt(-5+sin(x)^2)' with 'sqrt(5-sin(x)^2)', then 'integrate' can   
   > give a result.   
   >   
   > (cos(1/2*x)+sin(1/2*x))/(%e^x)^(1/3)   
   >   
   > If you simply rewrite it as (cos(1/2*x)+sin(1/2*x))/exp(x/3),   
   > then FriCAS can solve it.   
   >   
   > cos(1/3*x)^3/sqrt(%e^x)   
   >   
   > Same as previous one, rewrite it as 'cos(1/3*x)^3/exp(x/2)'.   
   >   
   > For other failures, 3 are errors, 8 are timeouts.   
      
   I believe it has been mentioned on sci.math symbolic that the radicands   
   of Timofeev's examples 5.85 (#421), 5.89 - 90 (#425 - #426), 5.98 - 99   
   (#434 - #435), and 5.109 (#446) are negative for all real x. Timofeev   
   may have been unaware of this because considerable work is involved in   
   plotting such integrands on paper with the help of a slide rule. If no   
   indication can be found in his book that such radicands were introduced   
   deliberately, I won't object if a consensus emerges to negate these six   
   in the Timofeev testsuite (briefly noting the what and why in comments),   
   but neither am I going to push the issue.   
      
   It should be noted, however, that among the six integrals involving   
   imaginary radicals, FriCAS seems to have problems only with 5.90 (#426)   
   and 5.109 (#446) for some reason. And ultimately, the system should of   
   course be enabled to handle such integrands anyway.   
      
   Your integrands involving algebraic powers of #e^x, which correspond to   
   Timofeev's examples 8.26 - 27 (#542 - #543) and 8.30 (#546), are written   
   as printed in his textbook, and so should not be modified for reasons   
   mentioned recently.   
      
   Martin.   
      
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