# 100 upvotes!

**Calculus**Level 5

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

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, \({ \text{Li} }_{ n }(a)=\displaystyle\sum _{ k=1 }^{ \infty }{ \dfrac { { a }^{ k } }{ { k }^{ n } } } \).

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.