On Tuesday, June 2, 2015 at 7:26:50 PM UTC+2, Gregory Bard wrote:
>
> However, I think the interface between Sage and Maxima is causing the 
> (incorrect) substitution of sqrt( cot(x)^2 ) = cot(x).
>

Something is happening in the interface, yes, but 

Interestingly, while I do not know Maxima, a colleague of mine does, and he 
> says that Maxima will not make this illegal substitution.
>

Well, Maxima will not solve it at all. I just confirmed with the newest 
version 5.36.1.
also using the abs_integrate package (which is not the culprit this time, 
surprise)

>
> It would be extremely useful if the bug could be fixed before the start of 
> the Fall semester, because I'm teaching the same course again. :-P
>

The fix in Sage will just change the result to integral( sqrt( cot(x)^2 ), 
x, pi/4, 3*pi/4 )
For a correct solution to be returned Maxima must be improved.
 
Regards,

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