## Camelia Integral on the fractional part function

Let be a positive integer and let denote the fractional part function, then calculate in closed-form the following Triple Integral :

${\int}_{0}^{1}{\int}_{0}^{1}{\int}_{0}^{1}{\mathrm{ln}}^{k}\left(xyz\right)\mathrm{\backslash bigg}\left\{\mathrm{\backslash bigg}\right(\frac{x}{y}\mathrm{\backslash bigg}{)}^{k}\mathrm{\backslash bigg}\left\}\mathrm{\backslash bigg}\right\{\mathrm{\backslash bigg}\left(\frac{y}{z}\mathrm{\backslash bigg}{)}^{k}\mathrm{\backslash bigg}\right\}\mathrm{\backslash bigg}\left\{\mathrm{\backslash bigg}\right(\frac{z}{x}\mathrm{\backslash bigg}{)}^{k}\mathrm{\backslash bigg}\}\mathrm{d}x\mathrm{d}y\mathrm{d}z$

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