A calculus problem by Hummus a

Calculus Level 3

\[ \large \displaystyle\int _{ 1 }^{ 2 }{ x\ln { (x-1) } \, dx } \]

If the integral above is equal to \( -\dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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