Integrating a function f(x) I am a bit confused about an integration that I came across. $f(x)$ is a function and we are integrating:
$$\int_0^t {df(x)\over f(x)} = \ln \left({f(t)\over f(0)}\right)$$
I am a confused because I was expecting an answer like $\ln(f(x)) - \ln(f(0))$

Technically,
$$\log(f(x))-\log(f(0))$$ is slightly different from $$\log\left(\frac{f(x)}{f(0)}\right)$$ because the latter also works when the two function valuations are negative.
You might prefer the expressions
$$\log(|f(x)|)-\log(|f(0)|)$$
or
$$\log\left(\left|\frac{f(x)}{f(0)}\right|\right)$$
but IMO they are not the best choice because they work for two valuations of different sign, though they should not (zero crossings are discouraged as this makes an improper integral).
