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Since the time of Euler, the dilogarithm and polylogarithmfunctions have been studied by many mathematicians who usedvarious notations for the dilogarithm function {text{Li}}_2(z). These functions are related to many othermathematical functions and have a variety of application. The mainobjective of this paper is to present corrected versions of twoequivalent factorization formulas involving the Legendre'sChi-function chi_2 and an evaluation of a class of integralswhich is useful to evaluate some integrals associated with thedilogarithm function.