Thanks for the report.

Git bisect points to
https://github.com/fricas/fricas/commit/1f42999f91ce516a8d027a61be4ecbf32ad2ada4

"Handle some elliptic integrals", June 14, 2022.
(Between 1.3.7 and 1.3.8)

Before this commit, the result is a integral sign
which means fricas proves it does not have elemental
integral, which is correct.

- Best,
- Qian

On 1/28/26 1:42 AM, Fabian wrote:
> Hello FriCAS group,
> 
> It looks like I found a bug in FriCAS:
> F:=integrate(acos(x^2),x)
> gives:
>       +--------+
>      |   4         2      2
> - 2 \|- x  + 1  + x acos(x )
> ----------------------------
>               x
> 
> D(F,x)-acos(x^2)
> gives the following instead of 0:
>        2
> -------------
>    +--------+
>  2 |   4
> x \|- x  + 1
> 
> I use FriCAS via https://sagecell.sagemath.org/ . Here is some Sage-code
> that produces the above output:
> 
> from sage.interfaces.fricas import fricas
> fricas.eval(
>     "F:=integrate(acos(x^2),x)"
> )
> print("F=\n",fricas("F"))
> fricas.eval("f:=D(F,x)-acos(x^2)")
> print("F'-acos(x^2)=\n",fricas("f"))
> 
> The FriCAS version is 1.3.12. (print(fricas.eval(")lisp |
> $build_version|") tells me this.)
> 
> The SageMath version is 10.8, Release Date: 2025-12-18. (version() tells
> me this.)
> 
> Fabian
> 
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