The Maxima team has opened two bug reports about this issue:

incorrect dilogarithm limit in definite integral & incorrect trig 
substitution:

https://sourceforge.net/p/maxima/bugs/4368/ and 
https://sourceforge.net/p/maxima/bugs/4369 


OHappyDay schrieb am Samstag, 7. September 2024 um 17:20:08 UTC+2:

> I have reported this to the Maxima team.
>
> wdjo...@gmail.com schrieb am Donnerstag, 5. September 2024 um 15:19:02 
> UTC+2:
>
>> On Thu, Sep 5, 2024 at 9:16 AM 'OHappyDay' via sage-support <
>> sage-s...@googlegroups.com> wrote:
>>
>>> I recently stumbled upon something that looks like a bug:
>>>
>>> Try to integrate the following function:
>>>
>>> f(x)=log(1-4*cos(x)+4)
>>> integrate(f,x,0,pi)
>>>
>>> According to the following video (
>>> https://www.youtube.com/watch?v=nscSDYApAjM) the result should be
>>>
>>> 2*pi*log(2)
>>>
>>> But my local Sage as well as online I get this result:
>>>
>>> 1/12*I*pi^2 + pi*log(3) - 1/2*pi*log(9/4) + 1/2*I*log(2)^2 - I*dilog(2) 
>>> + I*dilog(-1/2) + I*dilog(-2)
>>>
>>> which is a complex number instead.
>>>
>>
>> This could be a bug in Maxima:
>>
>> sage: CC(integrate(f,x,0,pi, algorithm='sympy'))
>>
>> 4.35517218060720
>>
>> sage: CC(integrate(f,x,0,pi, algorithm='maxima'))
>>
>> 4.44089209850063e-16 - 3.28986813369645*I
>>
>> sage: CC(2*pi*log(2))
>> 4.35517218060720
>>  
>>
>>>
>>> Similarly this function
>>>
>>> g(x)=log(1-cos(x)+1/4)
>>> integrate(g,x,0,pi)
>>>
>>> results in 
>>>
>>> 1/12*I*pi^2 - pi*log(3) + 1/2*pi*log(9/4) + 1/2*I*log(2)^2 - I*dilog(2) 
>>> + I*dilog(-1/2) + I*dilog(-2)
>>>
>>> although it should be ZERO. 
>>>
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>>>  
>>> <https://groups.google.com/d/msgid/sage-support/d3714f3c-b193-4d32-9d44-8a5a6d8ec5f1n%40googlegroups.com?utm_medium=email&utm_source=footer>
>>> .
>>>
>>

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