Integration in Finite Terms: Dilogarithmic Integrals
arXiv:2104.12504 · doi:10.1007/s00200-021-00518-3
Abstract
We extend the theorem of Liouville on integration in finite terms to include dilogarithmic integrals. The results provide a necessary and sufficient condition for an element of the base field to have an antiderivative in a field extension generated by transcendental elementary functions and dilogarithmic integrals. We also study algebraic independence of certain dilogarithmic integrals.