??????? ???????????? schrieb:
> To dev of FriCAS: apparently FriCAS cannot handle the key
> result of both papers, it causes infinite loop (or whatever):
> integrate(x/(x^2-1/5-2*%i/5)/(x^3-x)^(1/2), x)
If I remember correctly, Waldek Hebisch found that FriCAS could handle
this integral a few years ago, after some bugs had been eliminated.
> While it is elementary! Mathematica 13 can do it very fast, but
> not in elementary functions. It is interesting WHY FullSimplify
> does not see it from the math. 13 result, is it possible there is
> a simplification to elementary function possible or a constant
> difference in real part? Or is the result in the paper too big?
I suspect you are asking simply too much of Mathematica here.
> The other example that Mathematica 13 solves with insanely
> big result. Never seen anything like it (but again paper gives
> elementary result, DID not check FriCAS):
> Integrate[((5t^2+40^t+62)x+t^3+8t^2+70^t+144)/ (x-t)((2t+8)x+t^2+4t+18)( x^3-30x-56)^(1/2),x]
> P.S. After reading the papers I did not find the script to
> generate those but it should be there, of course.
[In the above, I have corrected your minus signs to ASCII.] In the
published paper, which you can find at the Acta Mathematica site for
download, this counterexample was withdrawn; the authors finally
managed to show that the antiderivative is elementary for at most 138
values of t (see the end of Section 16.3). What value did you try?