# Let's do some calculus! (48)

Calculus Level 5

$\large \int_0^1 {\left\{ \dfrac 1x \right\}}^{2017} \mathrm{d} x$

If the value of the above integral can be represented as

$\sum_{j=1}^{\infty} \dfrac{\zeta (j+A) - B}{ \binom{C + j}{j} }$

for positive integers $A, B$ and $C$, then evaluate $A+B+C$.

Notations:

Hint: Generalize for

$\int_0^1 {\left\{ \dfrac 1x \right\}}^{k} \mathrm{d} x$

where $k \ge 0$ is an integer.