I'm self teaching from Core Maths for Advanced Level by Bostock and Chandler. They say this:
$\int \frac{1}{ax + b} dx = \frac{1}{a} ln |ax + b| + K = \frac{1}{a} ln A|ax + b|$
There's no explanation of where the $A$ comes from, or where the constant of integration went. Can anyone explain how the equation is true, and what the motivation for doing this is?