Example 3. Find the integral $\int \frac{d x}{a x+b}$.
Solution.

$$
\int \frac{d x}{a x+b}=\int \frac{\frac{1}{a} d(a x+b)}{(a x+b)}=\frac{1}{a} \int \frac{d(a x+b)}{(a x+b)}=\frac{1}{a} \ln |a x+b|+C
$$