Integral with dilogarithm
- Tolaso J Kos
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Integral with dilogarithm
Let ${\rm Li}_2$ denote the dilogarithm function. Prove that:
$$\int_0^1 \frac{\left({\rm Li}_2(x)\right)^3}{x}\, {\rm d}x = \frac{15}{2}\zeta (3)\zeta(4)-9\zeta(2)\zeta(5)+\frac{51 \zeta (7)}{8}$$
$$\int_0^1 \frac{\left({\rm Li}_2(x)\right)^3}{x}\, {\rm d}x = \frac{15}{2}\zeta (3)\zeta(4)-9\zeta(2)\zeta(5)+\frac{51 \zeta (7)}{8}$$
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