Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Barton Willis
Date: Sat, 17 Jul 2010 08:39:32 -0500
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. Of course, an
alternative to returning a conditional is have diffdiv call asksign.
--Barton