[Maxima-bugs] [maxima:bugs] #4587 limit of integral expression incorrect, should be 1/e^2, not 0

[Robert D. <rob...@us...>]

Not entirely sure what's going on, but anyway I see
```
(%i26) n(x)/d(x);
                           x
                          ⌠
                   - %e x ⎮     %e t      1 t
(%o26)           %e       ⎮   %e     (1 - ─)  dt
                          ⎮               t
                          ⌡
                           %e
```
and `limit` appears to be looking at each of the terms; it gets 0 for the limit of the first term (correctly), and for the second it gets
```
                      inf
                     ⌠
                     ⎮      %e t      1 t
(%o27)               ⎮    %e     (1 - ─)  dt
                     ⎮                t
                     ⌡
                      %e
```
I speculate the `limit` is thinking that it can just multiply the two limits together, and then it gets 0. `limit` might be only looking to see if the result of the second  is not a `limit` noun expression, and going ahead if it doesn't see that. If those speculations are right, it might be relatively straightforward to get `limit` to return a noun expression. That would not be incorrect, but a little disappointing. 

Getting to the known result is easy via L'Hopital's rule, but I don't know what it would take to nudge `limit` to use it.


---

**[bugs:#4587] limit of integral expression incorrect, should be 1/e^2, not 0**

**Status:** open
**Group:** None
**Created:** Wed Jul 30, 2025 07:56 AM UTC by vsxbamboo
**Last Updated:** Wed Jul 30, 2025 04:15 PM UTC
**Owner:** nobody


```
(%i40)	n(x) := integrate((1-1/t)^t*%e^(%e*t), t, %e, x);
	n(%e+1);
	d(x) := %e^(%e*x);
	limit(n(x)/d(x), x, inf);
(%o37)	n(x):=integrate((1-1/t)^t*%e^(%e*t),t,%e,x)
(%o38)	integrate((1-1/t)^t*%e^(%e*t),t,%e,%e+1)
(%o39)	d(x):=%e^(%e*x)
(%o40)	0
```


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