Axiom doesn't seem to do the integral of sin(x^2), but both Maxima and Mathematica (per http://integrals.wolfram.com/ anyway) produce answers. Confirmed by Martin Rubey, and uploaded at his request to IssueTracker. CY fricas integrate(sin(x^2),
Type: Union(Expression(Integer),
However: Maxima 5.9.1.1cvs http://maxima.sourceforge.net Using Lisp CMU Common Lisp 19b (19B) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. This is a development version of Maxima. The function bug_report() provides bug reporting information. (%i1) integrate(sin(x**2),x); (sqrt(2) %i + sqrt(2)) x (%o1) sqrt(%pi) ((sqrt(2) %i + sqrt(2)) erf() 2 (sqrt(2) %i  sqrt(2)) x + (sqrt(2) %i  sqrt(2)) erf())/8 2 (%i2) (new) Bob McElrath?, Fri, 19 Aug 2005 11:13:26 0500 reply It's worth noting that both Maple and Mathematica produce the FresnelS?
function, which is defined in terms of this integral. However, the
Maxima answer appears to be correct as well.
Note that is a Dfinite function:
fricas f := sin(x^2)
Type: Expression(Integer)
fricas 4*x^3*f  D(f,
Type: Expression(Integer)
Thus integration should be "easy"... I browsed the web a little more and came to the conclusion that the Risch algorithm only deals with elementary functions whose integral is elementary, too. "Clearly" (looking at maxima's output or browsing the web), does not have an elementary antiderivative. Hence, I suspect that it should be treated just as , by thePatternMatchIntegration package. This would not be too difficult, probably.
Martin Although this does not really solve the original problem, I think I found a bug inINTPM . Currently, there is an operation:
pmComplexintegrate(f, x) == (rc := splitConstant(f, x)).const ^= 1 => (u := pmintegrate(rc.nconst, x)) case "failed" => "failed" rec := u::ANS [rc.const * rec.special, rc.const * rec.integrand] cse := (rec := matcherfei(f, x, true)).which cse = ERF => [rec.coeff * erf(rec.exponent), 0] "failed" It is pretty obvious that the third line should read: (u := pmComplexintegrate(rc.nconst, x)) case "failed" => "failed" instead. If we perform this change, we get instead of fricas complexIntegrate(%i/2*e^(%i*x^2),
Type: Expression(Complex(Integer))
the correct answer, same for fricas complexIntegrate(%i/2*e^(%i*x^2),
Type: Expression(Complex(Integer))
For some reason, it still won't do fricas complexIntegrate(sin(x^2),
Type: Expression(Integer)
Curiously, the pattern matcher is not even invoked in this case... Even if we enter the integral as fricas complexIntegrate(%i/2*e^(%i*x^2)+%i/2*e^(%i*x^2),
Type: Expression(Complex(Integer))
it fails, although in this case the pattern matcher is invoked. It would need to be invoked on each summand seperately, though. Martin There is another issue I don't quite understand. Currently axiom returns the whole integral unevaluated if it does not manage to evaluate it completely. If it were not for the bug #199, the following were an example:fricas integrate(exp(x)/x+exp(x^2)+1/log(x),
Type: Union(Expression(Integer),
Although axiom produces the intermediate result rinteg(i, f, x, h, comp) == not elem? i => integral(f, x)$F empty? rest(l := [mkPrimh(f, x, h, comp) for f in expand i]) => first l l Does this make sense? Martin partially fixed in FriCAS
Status: open => closed
