On Thu, Sep 5, 2024 at 9:16 AM 'OHappyDay' via sage-support <
sage-support@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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