Abstract
In this paper, the following multiple fractional part integrals and are calculated for non-negative integers and positive integer n, where denotes the fractional part of u and It is proved that has a closed form for non-negative integer . We also prove that ( and ) and can be expressed as linear combinations of the Riemann zeta function, logarithmic function and some binomial coefficients. In particular, has a closed form for . Moreover, some identities and recursive formulas of the above integrals are obtained.
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