Integral with dilogarithm

Calculus (Integrals, Series)
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Tolaso J Kos
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Integral with dilogarithm

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Post by Tolaso J Kos »

Let ${\rm Li}_2$ denote the dilogarithm function. Prove that:

$$\int_0^1 \frac{\left({\rm Li}_2(x)\right)^3}{x}\, {\rm d}x = \frac{15}{2}\zeta (3)\zeta(4)-9\zeta(2)\zeta(5)+\frac{51 \zeta (7)}{8}$$
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