Fractional part fun

Calculus Level 4

1{x}x3dx=aπbc \int_1^{\infty}\frac{\{x\}}{x^3}\, dx=a-\frac{\pi^b}{c}

The above integral is true for positive integers a,b,a, b, and cc.

What is the value of a+b+c?a+b+c?

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

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