Waldek Hebisch schrieb: > > Yes, FriCAS produced elementary results. I have now checked them > by differentiation. FriCAS 1.2.0 produced one wrong result > for INT(1/(x*log(x/a)+x)), x). This was silly bug (fixed in > trunk) which caused extra 'a' factor in the answer. In two > cases FriCAS is unable to simplify difference between integrand > and derivative of the integral -- both cases involve potentally > different branches of square roots. One is: > > +-----+ > | 1 > |----- > \|x + 1 1 > - atan(--------) + atan(----------------) > +-----+ +-----+ > | x | x +-----+ > |----- |----- \|x + 1 > \|x + 1 \|x + 1 > > The other is is similar, but bigger. >
This expression differentiates to
SQRT(x/(x+1))*(SQRT(1/(x+1)) - 1/SQRT(x+1))/(2*x)
which is zero everywhere except on the negative real axis for x < -1. (It is no delta function, however.)
The following table summarizes the performance data made available so far.
FriCAS has been stripped of the title! There is a tie now between FriCAS and Maple, and no clear winner emerges.
What about the others: Is Lady Maxima on her death bed already? And Sir Axiom? Is Sympy still nothing but a Dreikäsehoch? Has Mathematica gone fully Coca Cola already? Any one of them has a chance to become the one and only winner!