Another fractional part integral

Calculus Level 5

01{1x}x1xdx=Aγ+B \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 AA and BB. Find A+BA+B.

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