In this paper, we first evaluate unified finite multiple integrals whose integrand involves the product of the generalized hypergeometric function, general class of multivariable polynomials , the series expansion of multivariable A-function, a sequence of functions and the multivariable I-function. The arguments occurring in the integrand involve the product of factors of the form while that of , occurring herein involves a finite series of such coefficients. On account of the most general

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... re of the functions happening in the integrand of our integral, a large number of new and known integrals can be obtained from it merely by specializing the functions and parameters involved here. At the end, we shall see two corollaries.