Linear relations between logarithmic integrals of high weight and some closed-form evaluations

K. C. Au

The focus of our investigation will be integrals of form ${\int }_0^1{\log }^a(1-x){\log }^{b}x{\log }^c(1+x)/f(x)dx$, where $f$ can be either $x,1-x$ or $1+x$. We show that these integral…