Q:

Which derivative to use for an integral?

Does anyone know of a rule to tell which derivative to use when faced with an integral like this? (C is any constant, eg. 2400 or 4, etc).
$$\int \:\frac{C}{x}\mathrm{d}x$$
I know that $\ln(x) = \int\frac{1}{x}\mathrm{d}x$ so then $\int \:\frac{C}{x}\mathrm{d}x$ could equal $C\ln(x)$.
I also know that $\frac{1}{x}$ can be $x^{-1}$. 
Both the $\ln(x)$ and $x^{-1}$ give different answers, so employing the wrong one is a problem. So how do we know which one to use and what situation?
An example, $\int \:\frac{2.6}{x}$. Which "derivatie method" (excuse my lack of proper terminology) would I use if I am trying to get the integral?

A:

If we try to integrate $x^{-1}$ using the power rule it replaces the function with a constant because $x^0=1$. Since it is a constant, its derivative is not actually $x^{-1}$ so we know it doesn't work. Since $-1$ is the only value that doesn't follow the power rule it's the only special case you have to remember.

