>
>
> 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.)
>>
>
> It seems "domain: complex" causes the problem.
>
>  (%i1) display2d:false;
>
> (%o1) false
> (%i2)  integrate(sqrt(cot(x)^2),x);
>
> (%o2) 'integrate(abs(cot(x)),x)
> (%i3) domain:complex;
>
> (%o3) complex
> (%i4)  integrate(sqrt(cot(x)^2),x);
>
> (%o4) log(tan(x))-log(tan(x)^2+1)/2
>
> This may be worth reporting to Maxima.
>

Perhaps surprisingly, abs_integrate isn't involved in the mess-up?  Yes, 
definitely report upstream.

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