# Polylogs!

Calculus Level 5

$\large \int _{ 0 }^{ 1 }{ \dfrac {\text{Li}_2(x^3) }{ x^{ 2 } } \, dx }$

if the above integral is in the form $a\ln { \sqrt { b } } -\dfrac { \pi \sqrt { c } }{ d } -\dfrac16 { \pi }^{ f },$

where $$a,b,c,d$$ and $$f$$ are positive integers, find $$a+b+c+d+f$$.

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

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