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Calculus Level 5

\[\large \int_{0}^{1} \dfrac{(\ln x)^4}{(1-x)^4}\, dx = A\zeta(P)+B\zeta(Q)+C\zeta(R)\]

If the equation above is true for positive integers \(A\), \(B\), \(C\), \(P\), \(Q\), and \(R\), find \(A+B+C+P+Q+R\).

Notation: \(\zeta(\cdot) \) denotes the Riemann zeta function.

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