Background
Suppose $R(x)$ is a rational function with no positive real roots, and we want to integrate the following integral:
$$\int_0^\infty \frac{\log^n(x)}{R(x)} dx.$$
There's a trick that I've commonly seen where the integrand is multiplied by $\log(x)$ and this is integrated over $\gamma$, the keyhole contour together with the residue theorem.
$$\int_\gamma \frac{\log^{n+1}(z)}{R(z)} dz = 2\pi i\sum_{i}\operatorname{Res}_{z_i}\left(\frac{\log^{n+1}(z)}{R(z)}\right).$$
Question.
Is there a name for this technique?
I see on Wikipedia that there is a related example called "The square of the logarithm", but I'm looking for a term that I can look up in the index of a Complex Analysis text.
