Allow access to principal values of integrals

[kcrisman]

In this sage-support thread, the question was raised about accessing principal values of divergent integrals when they exist. This is in Maxima, but we currently raise an error if the integral is divergent. Some options mentioned in the thread were having another parameter, another method, or something else.

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/13511

[kcrisman]

comment:5

Perhaps more importantly, sometimes the principal value returned is correct even without considering improper integrals!

(%i1) integral(sec(x), x, -%pi/4, %pi/4);
                                              %pi  %pi
(%o1)                   integral(sec(x), x, - ---, ---)
                                               4    4
(%i2) integrate(sec(x), x, -%pi/4, %pi/4);
Principal Value
                         sqrt(2) + 2          sqrt(2) - 2
(%o2)                log(-----------) - log(- -----------)
                              2                    2

See #17608.

[nbruin]

comment:6

Replying to @kcrisman:

Perhaps more importantly, sometimes the principal value returned is correct even without considering improper integrals!

Isn't it a bug in maxima that it warns about Principal Value when it really is just the proper value?