# Primitive of Reciprocal of a x + b

## Theorem

$\displaystyle \int \frac {\d x} {a x + b} = \frac 1 a \ln \size {a x + b} + C$

## Proof

 $\displaystyle \int \frac {\d x} {a x + b}$ $=$ $\displaystyle \frac 1 a \int \frac {\map \d {a x + b} } {a x + b}$ Primitive of Function of $a x + b$ $\displaystyle$ $=$ $\displaystyle \frac 1 a \ln \size {a x + b} + C$ Primitive of Reciprocal

$\blacksquare$