Integrating abs(x)?



You can try pmint. Last I checked, you can download pmint from
http://wxmaxima.sourceforge.net/pmint.mac.
I don't know enough about how pmint works to know if my value for the
darboux polynomial of the absolute
value function is correct. So be careful!

Examples:

(%i8) load("pmint.mac")$
(%i9) put(abs, [lambda([u], u), true], 'darboux_poly)$
      gradef(abs(x), abs(x) / x)$

(%i11) pmint(abs(x),x);
(%o11) (x*abs(x))/2

(%i12) pmint(abs(6*x),x);
(%o12) 3*x*abs(x)

(%i13) pmint(x * abs(x/5),x);
(%o13) (x^2*abs(x))/15

(%i14) pmint(x^2 * abs(x^3),x);
Solution check failes!
(%o14) (x^3*abs(x)^3)/6

(%i15) ratsimp(diff(%,x));
(%o15) (x^2*abs(x)^3+x^4*abs(x))/2

Barton