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.

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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