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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Expansion of an integral

I have an integral of the form $$ I=\int_0^{\infty}{dx}\ln \bigg(1+\exp(-\frac{f(x)}{a})\bigg) $$ where $a$ is a positive constant and $f(x)$ is a regular and positive function such that $I$ is finite …