Another fractional part integral

Calculus Level 5

\[ \large \displaystyle\int _{ 0 }^{ 1 }{ \left\{ \dfrac { 1 }{ x } \right\} \dfrac { x }{ 1-x } \, dx=A\gamma } +B\]

The equation above holds true for integers \(A\) and \(B\). Find \(A+B\).

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