\[ \int_1^{\infty}\frac{\{x\}}{x^3}\, dx=a-\frac{\pi^b}{c}\]

The above integral is true for positive integers \(a, b,\) and \(c\).

What is the value of \(a+b+c?\)

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

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