This gives a lisp error
integrate(sqrt(k*t)*t,t);
The same is true if we give the integrand a different shape
integrate(k*t^2/sqrt(k*t),t);
Some other integrals are returned in noun form
integrate(sqrt(k*t)*t^(1/3),t);
So this does not seem to be a simplification issue but an actual
integration bug, for which I propose the following patch.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Index: sin.lisp
===================================================================
RCS file: /cvsroot/maxima/maxima/src/sin.lisp,v
retrieving revision 1.5
diff -u -r1.5 sin.lisp
--- sin.lisp 11 Mar 2004 04:55:24 -0000 1.5
+++ sin.lisp 31 Mar 2004 18:42:16 -0000
@@ -585,6 +585,7 @@
(DEFUN SUBST41 (EXP A B) (SUBST4 EXP))
+;; exp = a*t^r1*(c1+c2*t^q)^r2, where var = t.
(DEFUN CHEBYF (EXP VAR)
(PROG (R1 R2 D1 D2 N1 N2 W Q)
(COND ((NOT (SETQ W
@@ -601,6 +602,15 @@
((COEFFTT) (A FREEVAR)))
NIL)))
(RETURN NIL)))
+ (when (zerop1 (cdr (sassq 'c1 w #'nill)))
+ (return
+ (mul*
+ ;; This factor is locally constant as long as t and
+ ;; c2*t^q avoid log's branch cut.
+ (subliss w '((mtimes) a ((mexpt) var ((mtimes) -1 q r2))
+ ((mexpt) ((mtimes) c2 ((mexpt) var q)) r2)))
+ (integrator
+ (subliss w '((mexpt) var ((mplus) r1 ((mtimes) q r2)))) var))))
(SETQ Q (CDR (SASSQ 'Q W 'NILL)))
(SETQ
W
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ cut ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Wolfgang