Integral with dilogarithm
Posted: Fri Sep 02, 2016 11:01 am
Let ${\rm Li}_2$ denote the dilogarithm function. Prove that:
$$\int_0^1 \frac{\left({\rm Li}_2(x)\right)^3}{x}\, {\rm d}x = \frac{15}{2}\zeta (3)\zeta(4)-9\zeta(2)\zeta(5)+\frac{51 \zeta (7)}{8}$$
$$\int_0^1 \frac{\left({\rm Li}_2(x)\right)^3}{x}\, {\rm d}x = \frac{15}{2}\zeta (3)\zeta(4)-9\zeta(2)\zeta(5)+\frac{51 \zeta (7)}{8}$$