\[\large \int _{ 0 }^{ 1 }{ x{ H }_{ x }\, dx } =a+\dfrac { \gamma }{ b } -\ln { \sqrt { c\pi } } \]

If the equation above holds true for positive integers \(a,b\) and \(c\), find \(a+b+c\).

**Notations**:

\( H_n\) denotes the \(n^\text{th} \) harmonic number, \( H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n\).

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

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