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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 9,303 of 10,432   
   clicliclic@freenet.de to clicliclic@freenet.de   
   Re: New report on CAS integration tests.   
   24 Mar 17 20:02:12   
   
   clicliclic@freenet.de schrieb:   
   >   
   > This surprising variability should of course be analyzed and addressed   
   > by Maple users and developers.   
   >   
   > The integrator tests, however, should steer clear of such ambiguities,   
   > and the most natural way is to write integrands exactly as Timofeev   
   > wrote them.   
   >   
   > I notice this seemingly harmless kind of modification for the   
   > following Chapter 1 integrands in Albert's Timofeev file:   
   >   
   > Examples 14a,b and 15a,b (p. 26): INT(SIN(2*x)/(b^2*SIN(x)^2 + a^2), x),   
   > INT(SIN(2*x)/(b^2*SIN(x)^2 - a^2), x) and INT(SIN(2*x)/(b^2*COS(x)^2 +   
   > a^2), x), INT(SIN(2*x)/(b^2*COS(x)^2 - a^2), x); examples 22 and 27 (p.   
   > 27): INT(((1 - SQRT(x) + x)/x)^2, x) and INT(SIN(x)*SIN(x/4), x);   
   > example 40 (p. 28): INT(#e^(- x/2)*(#e^(x/2) - 1)^3, x); examples 41 and   
   > 43-45 (p. 35): INT(1/(x^2 - 6*x + 5), x) and INT((x + 2)/(x^2 - 4*x -   
   > 1), x), INT(1/(1 + (x + 1)^(1/3)), x), INT(1/((a*x + b)*SQRT(x)), x);   
   > examples 50, 52, 59 (p. 36): INT(1/SQRT(3*x^2 - 4*x + 5), x), INT((2*x +   
   > 1)/SQRT(2 + x - x^2), x), INT(SIN(2*x)*(a^2 - 4*COS(x)^2)^(3/4), x); and   
   > example 80 (p. 42): INT(x^2*ATAN(x)/(1 + x^2), x).   
   >   
   > I consequently suggest to correct all of them.   
   >   
      
   To this listing should be added example 81 (p. 42): INT(ACOS(SQRT(x/(x +   
   1))), x).   
      
   And it should be mentioned that these are the results of a visual   
   comparison of Timofeev's textbook and Albert's pdf-file based on   
   "TimofeevIntegrationProblems.nb" and dated 20.12.2014 21:00:58.   
      
   The integrands I see in a recent Maxima file are much much worse!   
      
   Martin.   
      
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