Appears to me diffs back: False not necessarily means wrong result. For: [23] diffs back: False integrand: x*log(x + sqrt(x^2 + 1))*arctan(x)/sqrt(x^2 + 1) antideriv: sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1))*arctan(x) - x*arctan(x) - 1/2*log(x + sqrt(x^2 + 1))^2 + 1/2*log(x^2 + 1) maxima : (sqrt(x^2 + 1)*log(x + sqrt(x^2 + 1)) - x)*arctan(x) + 1/2*log(x + sqrt(x^2 + 1))^2 - log(x + sqrt(x^2 + 1))*arcsinh(x) + 1/2*log(x^2 + 1)
Test: sage: ex=x*log(x + sqrt(x^2 + 1))*arctan(x)/sqrt(x^2 + 1);inte=integrate(ex,x);back=inte.derivative(x) sage: t1=(ex-back).full_simplify() sage: t1 ((2*x^2 + 1)*arcsinh(x) - (2*x^2 + 1)*log(x + sqrt(x^2 + 1)) + 2*sqrt(x^2 + 1)*(x*arcsinh(x) - x*log(x + sqrt(x^2 + 1))))/(2*x^3 + (2*x^2 + 1)*sqrt(x^2 + 1) + 2*x) sage: CC(t1(x=5)) -1.09303758073658e-16 sage: CC(t1(x=14.13)) 0.000000000000000 According to Wolfram Alpha |t1| simplifies to 0: http://www.wolframalpha.com/input/?i=%28%282*x^2+%2B+1%29*arcsinh%28x%29+-+%282*x^2+%2B+1%29*log%28x+%2B+sqrt%28x^2+%2B+1%29%29+%2B+2*sqrt%28x^2+%2B+1%29*%28x*arcsinh%28x%29+-+x*log%28x+%2B+sqrt%28x^2+%2B+1%29%29%29%29%2F%282*x^3+%2B+%282*x^2+%2B+1%29*sqrt%28x^2+%2B+1%29+%2B+2*x%29 Result: 0 This is modulo bugs in .full_simplify(). On Wed, Sep 04, 2013 at 10:01:07AM -0700, Peter Luschny wrote: > Recently two integration test suites were discussed at sci.math.symbolic > [1], [2]. > > I executed the tests with Sage and put the results on my webpage [3]. > Not all results are favorable for Sage. Maybe this is worth to be > noted by some Sage developers. > > Peter > > [1] > https://groups.google.com/d/msg/sci.math.symbolic/UB0udwILOSw/msxc57stRM8J > [2] > https://groups.google.com/d/msg/sci.math.symbolic/D9W45zQTY3U/nIxsBZ-4RasJ > [3] http://luschny.de/math/quad/IntegralTestsSage.html > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
