# Log and exponential integral

Calculus Level 5

$\large \int_0^\infty \dfrac{x^3}{e^x - 1} \ln(e^x - 1) \, dx = \pi^A \zeta(B) + C \zeta(D)$

If $$A,B,C$$ and $$D$$ are positive integers such that the equation above holds true, find $$A+B+C+D$$.

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

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