>> Albert used Maxima 5.28 whereas I used Sage 5.10. I do not know which >> Maxima version Sage 5.10 uses. They might be different.
> The Maxima integrator would be undergoing noticeable development then. A > pleasant surprise.
Well, I don't know. I just switched from Sage 5.10 to 5.11 and there are differences with regard to the Charlwood problems! Problem 8 for example now has a monster solution; so long that I did not care to check if it is right or wrong.
> After sign inversion the Maxima result appears to be correct on > the real axis.
Yes. And what about
diff(-1/4*sqrt(2)*arctanh(-1/2*(tan(x)^2-1)*sqrt(2)/sqrt(tan(x)^4+1)),x) = tan(x)/sqrt((tan(x))^4+1) versus diff(-1/4*sqrt(2)*arcsinh(cos(2*x)),x) = sin(2*x)/sqrt(cos(4*x)+3)
tan(x)/sqrt((tan(x))^4+1) = sin(2*x)/sqrt(cos(4*x)+3) on the real axis?
> But then Maxima doesn't claim to deliver antiderivatives for the > entire complex plane, or does it?
What are rules of the game anyway: Does the 'Charlwood test' require antiderivatives for the entire complex plane or only for the real line? Charlwood writes: "We consider integrals of real elementary functions of a single real variable in the examples that follow."