Answer
$$
\begin{aligned}
\int \frac{a x}{x^{2}-b x} d x=a \ln |x-b|+C
\end{aligned}
$$
where $C$ is an arbitrary constant.
Work Step by Step
$$
\begin{aligned}
\int \frac{a x}{x^{2}-b x} d x&=\int \frac{a x}{x(x-b)} d x \\
&=\int \frac{a}{x-b} d x \\
&=a \ln |x-b|+C
\end{aligned}
$$
where $C$ is an arbitrary constant.