> atan((exp(x) + x + 1)/(exp(x) - x - 1))
>
> There are two kernels here (exp(x) and x).  I am not sure
> if Rioboo is used here, but at least some simplification
> is done.

I checked this example, the "Rioboo" (aka log2atan) is not used
here, for rewriting "i*log((A+i*B)/(A-i*B))" to sums of arc-tangents,
it returns "2*atan(A/B)" because A and B are not both polynomials
of x.

>> I get it that x and sqrt(x) can both appear as kernels; is it possible
>> that there are three or more kernels?

My answer to my question: in general, if there are more than 2
non-constant kernels, the log2atan function just return "2*atan(A/B)",
and the selection of kernel is not relevant.
The exception is that when kernels are [x,sqrt(x)] (or [g(x),sqrt(g(x))],
because "univariate(x,first kernels sqrt x)" doesn't return "?^2".
How to solve this problem?

Examples are compose rational function f with other function g:

f := (2560*x^3 - 400*x^2 - 576*x - 84)/(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9)
g x == sqrt x -- or g x == sqrt exp x
h == eval(f, x= g x)*D(g x , x)
integrate(h,x)
-- if there's only one atan in the result, then it's not continuous.

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