# Who's up to the challenge? 49

Calculus Level 5

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

If the integral above can be expressed as $-\left[ \dfrac { a }{ b } +\dfrac { { \pi }^{ c } }{ d } \right] +\ln { f },$

where $$a,b,c,d$$ and $$f$$ are positive integers, with $$a,b$$ coprime, 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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