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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