Who's up to the challenge? 25

Calculus Level 5

∫01{1x}3dx=−HU−Mγ+M1U1ln⁡(Sπ)−Bln⁡A\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, AA is the Glaisher–Kinkelin constant, all other variables are positive integers, and all the fractions mentioned are coprime.

Find H+U+M+M1+U1+S+B.H+U+M+{ M }_{ 1 }+{ U }_{ 1 }+S+B.

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

This is a part of "Who's up to the challenge?"

Hamza A by Hamza A
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