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A class of definite integrals involving a quotient function with a reducible polynomial, logarithm and nested logarithm functions are derived with a possible connection to contact problems for a wedge. The derivations are expressed in terms of the Lerch function. Special cases are also derived in terms fundamental constants. The majority of the results in this work are new.

Mellin Transform of Logarithm and Quotient Function with Reducible Quartic Polynomial in Terms of the Lerch Function