Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Robert Dodier
Date: Sat, 17 Jul 2010 12:14:22 -0600
On 7/17/10, Barton Willis <willisb at unk.edu> wrote:
> I agree with Watson of Sherlock Holmes fame that "Singularity is
> almost invariably a clue." Accordingly, I would say that
>
> (%i1) integrate(cos(a*x),x);
> (%o1) sin(a*x)/a
>
> is suboptimal. The function diffdiv (defined in sin.lisp) is, I think,
> largely responsible for integration by substitution--it would be great
> to patch diffdiv to make it be more careful. And that project might
> not be all that difficult. If diffdiv returned conditional expressions,
> the more challenging task would be to patch the rest of Maxima to
> handle the conditional expressions more gracefully.
I'm 100% in favor of such a project.
> Of course, an alternative to returning a conditional is have diffdiv call asksign.
Well, I'm no big fan of asksign, but calling asksign would at least
be consistent with the behavior of other parts of Maxima
(pending the widespread use of conditional expressions as
described above).
best
Robert Dodier