For linear divergence, quad_qagi issues a console
warning and some error code number > 2 as
a warning.
-----------------------
Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
(%i1) quad_qagi(x,x,0,inf);
***MESSAGE FROM ROUTINE DQAGI IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 5
*
***END OF MESSAGE
(%o1) [0.49999999442512,2.2894791249616908E-5,885,5]
----------------------------------
But for exponential divergence, there is no console warning, and
an error code = 0 is returned. The user needs to see the occurrence
of #INF in the returned answer to infer the software/machine limit has
been reached.
----------------------------------------------
(%i2) quad_qagi(%e^x,x,0,inf);
(%o2) [1..#INF00e+000E+2288952,1..#INF00e+000E+2288952,75,0]
------------------------------------------
Ted Woollett