Goursat's theorem on pseudo-elliptic integrals is generalized to cube-root cases via order-3 Möbius automorphisms that decompose the integrand into two elementary pieces and one generically transcendental piece on a genus-1 curve.
Bronstein,Symbolic Integration I: Transcendental Functions, 2nd ed., Algorithms and Computation in Mathematics, vol
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A Generalisation of Goursat's Algorithm for Integration in Finite Terms
Goursat's theorem on pseudo-elliptic integrals is generalized to cube-root cases via order-3 Möbius automorphisms that decompose the integrand into two elementary pieces and one generically transcendental piece on a genus-1 curve.