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Comparison of three different regularization methods of calculating theone-loop effective Heisenberg-Euler Lagrangian of quantum electro-dynamics(QED) is employed to derive some interesting integrals involving the asymptoticexpansion of $\ln \Gamma_1(x+1)$, the generalized $\Gamma$ function. Here it isthe constant $L_1$ that will enable us to calculate some integrals which areuseful in mathematics as well as in physics.

Evaluation of Some Integrals Following from $L_1$, the Constant of the Asymptotic Expansion of $\ln \Gamma_1 (x+1)$, Originating from Physics (QED)