If \( \int\left(e^{2 x}+2 e^{x}-e^{-x}-1\right) e^{\left(e^{x}+e^{-x}\right)} d x=g(x) e^{\left(e^{x}+e^{-x}\right)}+c \…

If \( \int\left(e^{2 x}+2 e^{x}-e^{-x}-1\right) e^{\left(e^{x}+e^{-x}\right)} d x=g(x) e^{\left(e^{x}+e^{-x}\right)}+c \) where \( \mathrm{c} \) is a constant of integration, then \( g(0) \) is equal to :

[JEE Main 2020, 5 Sep (Shift 1)]