# Who's up to the challenge? 53

Calculus Level 5

$\large \int_0^1 \dfrac{ (\ln x)^2 \; \text{Li}_3 (x)}{1-x} \, dx = (\zeta(b))^a - \zeta (c)$

If the equation above holds true for positive integers $$a,b$$ and $$c$$, find $$a+b+c$$.



Notations:

• $$\zeta(\cdot)$$ denotes the Riemann zeta function.
• $${ \text{Li} }_{ n }(a)$$ denotes the polylogarithm function, $${ \text{Li} }_{ n }(a)=\displaystyle\sum _{ k=1 }^{ \infty }{ \frac { { a }^{ k } }{ { k }^{ n } } }.$$
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