Re: [Maxima-discuss] Value of integrate ((log (1 - t)) / t, t, 0, x)?

[Raymond T. <toy...@gm...>]

On 7/20/25 9:39 AM, Raymond Toy wrote:

> On 7/20/25 8:36 AM, Richard Fateman wrote:
>
>> works for me in 5.46.0.
>> -li[2](x)
> Clearly, it's a change since then.

For future reference, see https://sourceforge.net/p/maxima/bugs/4581/.

The Risch integrator is used and something weird happens substituting in 
the limits for the definite integral. I think.

>>
>> On Sun, Jul 20, 2025 at 11:25 AM Raymond Toy <toy...@gm...> 
>> wrote:
>>
>>     I was running update_examples in MathFunctions.texi.m4. One of
>>     the examples is |integrate ((log (1 - t)) / t, t, 0, x);|. The
>>     current manual says it's |-li[2](x)|, if we assume |x>0|.
>>
>>     I can't get this answer at all. But |diff(-li[2](x),x)| is the
>>     integrand.
>>
>>     The best I can get is for 0 < x < 1 the integral is
>>
>>     |(%i27) integrate ((log (1 - t)) / t, t, 0, x); Is x positive,
>>     negative or zero? pos; Is x - 1 positive, negative or zero? neg;
>>     2 1 log(1 - x) (2 log(x) - 2 log(x - 1)) + log (1 - x) - 2 li (-
>>     ─────) 2 x - 1 (%o27)
>>     ───────────────────────────────────────────────────────────────────
>>     2 2 %pi + ──── 6 |
>>
>>     However,
>>
>>     |(%i36) factor(logcontract(ratsimp(diff(%o27,x)))); log(1 - x)
>>     (%o36) ────────── x |
>>
>>     This has the wrong sign.
>>
>>     I guess this is a new bug.
>>
>>     &#8203;
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