We can use this to express a principal values integral as $$\begin{equation} {\cal P}\int_{0}^{\infty} \frac{f(k)dk}{k^2-k_0^2} = \int_{0}^{\infty} \frac{(f(k)-f(k_0))dk}{k^2-k_0^2}, \tag{26} \end{equation}$$ where the right-hand side is no longer singular at $k=k_0$, it is proportional to the derivative $df/dk$, and can be evaluated numerically as any other integral.

Such a trick is often used when evaluating integral equations.