Fractional part integration

Calculus Level 4

1{x}x5dx \large \int_1^\infty \dfrac{\{ x \}} {x^5} \, \mathrm{d}x

If the value of the integral above is equal to 1AπBC\dfrac1A - \dfrac{\pi^B}C for positive integers AA, BB and CC, find A+B+CA+B+C.

Bonus: Find the general form of 1{x}xndx \displaystyle \int_1^\infty \dfrac{\{x\}}{x^n} \, \mathrm{d}x .

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

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