\[ \DeclareMathOperator{li}{li\,} \large \displaystyle\int _{ 0 }^{ 1 }{ { 2 }^{ x }\log _{ 2 }{ x } \, dx } =\dfrac { H\gamma -\li(U)+M\ln { (\ln { { M }_{ 1 } } ) } }{ (\ln S)^{U_1} } \]

The equation above holds true for positive integers \(H,U,M,M_1,U_1,S\). Find \(H+U+M+M_1+U_1+S\).

**Notations**:

\( \DeclareMathOperator{li}{li\,} \li(\cdot)\) denotes the Logarithmic integral.

\( \gamma\) denote the Euler-Mascheroni constant, \(\gamma \approx 0.5772 \).

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