two different results with same numeric integral

[kcrisman]

Reported by Nicolas Privault via Rado Kirov:

sage: integrate(x^(0.5)*e^(-x-x^2),x,0,infinity).n()
0.886226925452758

sage: integrate(x^(1/2)*e^(-x-x^2),x,0,infinity).n()
0.32015709036013135

which give two different results, and the second one is correct.

Upstream: Reported upstream. No feedback yet.

CC: @orlitzky

Component: calculus

Stopgaps: #12732

Issue created by migration from https://trac.sagemath.org/ticket/11493

[kcrisman]

comment:1

Here is what is going on.

(%i16) integrate(x^(1/2)*%e^(-x-x^2),x,0,inf);
                           inf
                          /                 2
                          [              - x  - x
(%o16)                    I    sqrt(x) %e         dx
                          ]
                          /
                           0

(%i18) integrate(x^(.5)*%e^(-x-x^2),x,0,inf);
<snip lots of these>
rat: replaced 0.5 by 1/2 = 0.5
                                   sqrt(%pi)
(%o18)                             ---------
                                       2

[kcrisman]

Description changed:

--- 
+++ 
@@ -8,9 +8,4 @@
 0.32015709036013135
 
 which give two different results, and the second one is correct.
-
-Strangely again, one also has
-
-sage: integrate(x^(0.5)*e^(-x),x,0,infinity).n()
-0.886226925452758
 ```

[kcrisman]

comment:2

The other thing was correct, I believe, so I'm not sure what the poster thought was wrong with it.

sage: numerical_integral(x^(0.5)*e^(-x),0,100000)
(0.88622692749267307, 4.3485198683228606e-07)

[kcrisman]

Upstream: Reported upstream. Little or no feedback.

[kcrisman]

comment:3

This is now reported at this Maxima ticket.

[roed314]

Stopgaps: #12732

[roed314]

Changed upstream from Reported upstream. Little or no feedback. to Reported upstream. No feedback yet.

[kcrisman]

comment:7

#13718 may be related.