= Complex logarithm on the negative real axis
{title2=$\log x=\log|x|+(2k+1)i\pi,\quad x<0$}
A continuous choice of <complex logarithm> on a negative real interval has a fixed integer $k$ in the displayed expression. The choice with argument $\pi$ is the upper-bank boundary value of the <principal logarithm>; the usual analytic principal-branch domain itself excludes the negative axis. Consequently, integrating a real weight times that logarithm adds $(2k+1)i\pi$ times the integral of the weight to the real logarithmic integral. The branch choice must be stated.
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