# Time for easier problems

Calculus Level 3

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

If the value of the integral above is equal to $\text{Li}_a(be)-\zeta(c),$ where $$a,b$$ and $$c$$ are positive integers, find $$a+b+c$$.

Notation:

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