[Maxima-bugs] [maxima:bugs] #4581 integrate ((log (1 - t)) / t, t, 0, x) is wrong

[Barton W. <wil...@us...>]

...and one more thing: what is the magic in `ldefint` that makes the following correct?

~~~
(%i6) ldefint((log (1 - t)) / t, t,0,x);

INTEGRALLOOKUPS: Found integral MEXPT.
INTEGRALLOOKUPS: Found integral MEXPT.
INTFORM: found 'INTEGRAL on property list
INTEGRALLOOKUPS: Found integral MEXPT.
INTFORM: found 'INTEGRAL on property list
INTEGRALLOOKUPS: Found integral MEXPT.
INTFORM: found 'INTEGRAL on property list
INTEGRALLOOKUPS: Found integral MEXPT.
INTFORM: found 'INTEGRAL on property list
INTEGRALLOOKUPS: Found integral MEXPT.
                                                         2
                                                      %pi
(%o6)                log(1 - x) log(x) + li (1 - x) - ────
                                           2           6
(%i7) limit(%,x,0,plus);
(%o7)                                  0
(%i8) diff(%o6,x);
                                  log(1 - x)
(%o8)                             ──────────
                                      x

~~~


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**[bugs:#4581] integrate ((log (1 - t)) / t, t, 0, x) is wrong**

**Status:** open
**Group:** None
**Labels:** integrate 
**Created:** Sun Jul 20, 2025 05:19 PM UTC by Raymond Toy
**Last Updated:** Thu Jul 24, 2025 11:50 AM UTC
**Owner:** nobody


In current maxima, we have
```maxima
(%i1) display2d:false;

(%o1) false
(%i2) integrate ((log (1 - t)) / t, t, 0, x);
Is x positive, negative or zero?

pos;
Is x-1 positive, negative or zero?

neg;

(%o2) (log(1-x)*(2*log(x)-2*log(x-1))+log(1-x)^2-2*li[2](-(1/(x-1))))/2+%pi^2
                                                                        /6
```
According to the user manual, this used to return `-li[2](x)`.

If you differentiate `%o2` and manipulate it, you get the negative of the integrand.



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