Let's do some calculus! (47)

Calculus Level 5

01{1x2017}dx\large \int_0^1 \left\{ \dfrac{1}{\sqrt[2017] x} \right\} \, \mathrm{d}x

If the value of the above integral can be represented in the closed form as abζ(c)\dfrac{a}{b} - \zeta (c) where aa and bb are co-prime integers, then evaluate a+b+ca+b+c.

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