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$\large \int _{ 0 }^{ 1 }{ \dfrac {(\text{Li}_2(x) )^2 }{ { x }^{ 2 } } \, dx }=h\zeta (u)-n\zeta (d)-\dfrac { r }{ e } \zeta (d_1)$

If the equation above holds true for positive integers $h,u,n,d,r,e$ and $d_1$ , where $r$ and $e$ are coprime, find $h+u+n+d+r+e+d_1$ .

Notations :

• $\zeta(\cdot)$ denotes the Riemann zeta function .

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