Explicit evaluation of some integrals involving polylogarithm functions

Abstract

In this paper, we give explicit evaluation for some integrals involving polylogarithm functions of types ${\int }_0^x{t}^{m}L{i}_p(t)\mathrm{d}t$ and ${\int }_0^x{\log }^m(t)L{i}_p(t)\mathrm{d}t$. Some more integrals involving the logarithm function will also be derived.

23 pages