Integrating fractions

The idea

$\int \frac{1}{ax + b}\,dx = \frac{1}{a}\ln|ax + b| + c$. More complicated fractions are split into partial fractions first, then each part integrates to a logarithm.

1. If the denominator factorises, split into partial fractions.
2. Integrate each term: $\frac{k}{ax + b} \to \frac{k}{a}\ln|ax + b|$.
3. Combine the logs with the log laws.

Watch out Divide by the coefficient of $x$ in the denominator.