Binet's second formula, Hermite's generalization, and two related identities

Abstract Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these can be used prove Binet’s second formula for logarithm gamma function. Here, we show that other integral leads a specific case Hermite’s generalization formula. From analogs Legendre’s integrals, with replaced by cosines, obtain integration identities logarithms trigonometric functions. Using identities, then subsequently derive generalizations formulas complex logarithm.