(C1) defint(exp(a*x),x,0,inf);
Is a positive, negative, or zero?
zero;Principal Value
(D1) 0
This isn't a PV integral; the integral diverges when
a == 0.
(C2) build_info();
Maxima version: 5.9.0
Maxima build date: 19:10 2/9/2003
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL-2-5.0
Robert Dodier
2006-04-10
Harald Geyer
2008-03-25
Logged In: YES
user_id=929336
Originator: NO
Still observed in 5.14.0 and cvs HEAD from 2008-03-25
Dieter Kaiser
2009-05-27
The behavior has changed:
The sign of a is unknown. Maxima returns a noun form:
(%i3) defint(exp(a*x),x,0,inf);
(%o3) 'integrate(%e^(a*x),x,0,inf)
The sign of a is negative. We get the correct solution:
(%i4) assume(a<0)$
(%i5) defint(exp(a*x),x,0,inf);
(%o5) -1/a
The sign of the parameter b is positive. The integral is divergent:
(%i6) assume(b>0)$
(%i7) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
-- an error. To debug this try debugmode(true);
Up to here the solutions are correct and consistent. We assume a paramter less or equal zero and get a divergent result. I think, this should give a noun form too:
(%i10) forget(a<0)$
(%i11) assume(a<=0)$
(%i12) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
-- an error. To debug this try debugmode(true);
This is again correct. The integral is divergent when b is greater or equal zero:
(%i13) forget(b>0)$
(%i14) assume(b>=0)$
(%i15) defint(exp(b*x),x,0,inf);
defint: integral is divergent.
-- an error. To debug this try debugmode(true);
Perhaps we can change the one open case for a parameter a<=0. Then all cases will be correct.
Dieter Kaiser