There is an integral which Sage correctly numerically integrates, and which 
Sage symbolically gets very wrong. William and I looked into this during 
Sage Days 68, and he discovered that, in fact, Maxima gets this integral 
very wrong as well. (More correctly, the particular configuration and 
version of Maxima built into Sage gets the integral very wrong. Some 
setting might be incorrect or badly chosen.)

The integral of sqrt( cot(x)^2 ) dx for pi/4 < x < 3pi/4 is not too bad to 
compute by hand. The answer is the logarithm, base e, of 2. The numerical 
integration in Sage agrees.

Maxima thinks that the answer is instead zero. (Or more correctly, the 
particular configuration and version of Maxima built into Sage thinks the 
answer is zero.)

Please see the attached sagews worksheet. 

Is there anyone on this list who knows Maxima in general, and the 
connections/interface between Maxima and Sage in particular?
---Greg

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Attachment: The Bug In Maxima.sagews
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