https://arxiv.org/abs/2605.04978
Exhaustive Symbolic Integration: Integration by Differentiation
and the Landscape of Symbolic Integrability
Freshly published, at 2026 May 6.
Most interesting quote:
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while 232 (integrals, out of 49538) resist both SymPy and Mathematica
even at 600s. Those 232 were then passed to FriCAS, which solves 218.
This shows that most failures of SymPy, Mathematica and RUBI are
implementation-coverage gaps rather than evidence that no elementary
antiderivative exists. FriCAS solves all x^x type and f(x)^g(x)
integrals that defeat the other three engines. By contrast, RUBI
solves none of the 232 integrals that SymPy and Mathematica leave
unsolved; as a pattern library designed for textbook integral forms,
it does not aim to cover these deeply nested exp-log towers.
......
Both of these (RUBI failures in RUBI test suite) involve deeply
nested log/exp compositions of the kind that fall through the
gaps of rule-based systems but lie squarely within ESI’s
catalogued space. FriCAS also solves them.
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- Qian