Wow Integrable

$\large \int \frac{e^x + e^{-x} - 1}{(e^x \sin x + \cos x)(\cos x - \sin x e^{-x} ) } \, dx$

If the indefinite integral above is of the form $\ln \left | \dfrac{e^x \sin x + A\cos x}{e^x \cos x + B\sin x}\right | + C,$

where $A$ and $B$ are constants and $C$ is the arbitrary constant of integration, what is the value of $A+ B?$