Integration in Finite Terms: Dilogarithmic Integrals
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.
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