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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.              --- SoupGate-Win32 v1.05        * Origin: you cannot sedate... all the things you hate (1:229/2)    |
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