Fractional part integration

Calculus Level 5

\[ \large \int_1^\infty \dfrac{\{ x \}} {x^5} \, \mathrm{d}x \]

If the value of the integral above is equal to \(\dfrac1A - \dfrac{\pi^B}C \) for positive integers \(A\), \(B\) and \(C\), find \(A+B+C\).

Bonus: Find the general form of \( \displaystyle \int_1^\infty \dfrac{\{x\}}{x^n} \, \mathrm{d}x \).

Clarification: \(\{x\}\) denotes the fractional part function.

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