d(x) = *IntegralSign(b^(-x/c) / (f + ax))dx
a, b, c, f are constants
I'm stumped. A little help
The Mathematic site gives the answer in terms of the error function, which can only be approximated. But let's see what your substitution does.
$\displaystyle \int \frac{b^{-x/c}}{f + ax}~dx$
Let $\displaystyle u = f + ax \implies dx = \frac{1}{a}~du$
So
$\displaystyle \int \frac{b^{-x/c}}{f + ax}~dx = \int \frac{b^{-(f - u)/(ac)}}{u}~\frac{du}{a}$
$\displaystyle = \int \frac{b^{-f/(ac)}b^{u/(ac)}}{u}$
(which is pretty much the same form as you started with.)
I can see no way to integrate this (barring some kind of approximation.)
-Dan