# Fractional part integration

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

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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