Integral of ln(x^2)dx, from -5 to 99
Success with this integral and the time it takes will completely depend on the method used.
If you have an HP prime, looks like the fastest would be to do this in CAS mode (which will give you the exact result almost instantly). Then you can copy it in home mode to get the approximate value.
The Prime uses Giac for its CAS AFAIK, which you can also use on computers.
https://www-fourier.ujf-grenoble.fr/~parisse/giac.html(There is a web version if you want to quickly test it:
https://www-fourier.ujf-grenoble.fr/~parisse/xcasen.html )
integrate(ln(x^2),x,-5,99)
will give you: 5ln(25)+198ln(99)-208≈717.928109451
I tried with Maxima (both symbolic with integrate() and numeric integration with romberg(), and both failed.)
Also tried with Yacas (
http://www.yacas.org/ ), that I rarely use. Contrary to xcas/giac, it fails to solve the symbolic integration (with: Integrate(x,-5,99) Ln(x^2) ), but manages the numeric integration (with: NIntegrate(x,-5,99) Ln(x^2) ), it takes several seconds though, and is not very accurate (gives 717.92810937).