Who's up to the challenge? 28

Calculus Level 5

\[\displaystyle\int _{ 0 }^{ 1 }{ \int _{ 0 }^{ 1 }{ \left\{ \dfrac { k }{ x-y } \right\} \left\{ \dfrac { 1 }{ x } \right\} \left\{ \dfrac { 1 }{ y } \right\} \, dx\; dy } } =\dfrac { H }{ U } (M-{ M }_{ 1 }\gamma ^{ U_{ 1 } })^{ S }\]

Let \(k\) be a positive real number that satisfy the equation above, where \(H,U,M,M_1,U_1,S\) are positive integers and \(H,U\) coprime.

Find \(H+U+M+M_1+U_1+S\).

Notations:


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