Who's up to the challenge? 29

Calculus Level 5

0101x{11xy}dx  dy=Aζ(B)C \large \displaystyle\int _{ 0 }^{ 1 }{ \displaystyle\int _{ 0 }^{ 1 }{ x\left\{ \dfrac { 1 }{ 1-xy } \right\} \, dx\; dy } } =A-\dfrac { \zeta (B) }{ C }

If the equation above holds true for positive integers A,BA,B and CC, find A×B×CA\times B \times C.

Notations:


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