Computation of an integral of a rational function over the skeleton of unit polycylinder in $\mathbb C^{n}$ by means of the Mellin transform

With the help of the Mellin transform we give a simple calculation of an integral of rational functions in several independent parameters aerlier appeared in [2]. The efficiency of this transform is due to the fact that calculation the degree of the polynomial acts as the degree of a monomial. In 2008, G. P. Egorychev and E.V. Zima [5] for the first time successfully used the Mellin transform in the theory of rational summation. The possibility of its application in the analysis and computation of integrals with different types of rational functions is discussed.