I found this strange one while watching a mit integration bee video, $\int_{\log 1/2}^{\log2}{\sqrt[3]{x+sin(x)}}\space\mathrm{d}{x}$.
Although it is quite clear that the definite integral is zero, the antiderivative itself seemingly lies outside modern CASes' grasp: Axiom admits that it can neither compute it nor prove it being non-elementary, Mathematica fails similarily.
Notably, replacing cubic root with square root does not make the problem simplier, as both CASes fail there as well...