Who's up to the challenge? 25

Calculus Level 5

\[\int _{ 0 }^{ 1 }{ \left\{ \frac { 1 }{ x } \right\} ^{ 3 } } dx=−\frac { H }{ U } −Mγ+\frac { { M }_{ 1 } }{ U_1 } \ln { (Sπ) } −B\ln { A } \]

In the equation above, \(A\) is the Glaisher–Kinkelin constant, all other variables are positive integers, and all the fractions mentioned are coprime.

Find \(H+U+M+{ M }_{ 1 }+{ U }_{ 1 }+S+B.\)

Note: \(\{x\}\) denotes the fractional part of \(x.\)


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