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Jul 20, 2019 at 19:30 comment added sonicboom I am now back home and have access to Mathematica. It seems it can't evaluate the integral at all now that I have included the logarithmic term. Even just trying to evaluate the indefinite integral is failing, I might have to just try and do it numerically with NIntegrate and plot it instead.
Jul 20, 2019 at 19:23 comment added sonicboom You are correct, I just realised I am missing a $\frac{1}{2\pi}\log(t)$ in the integral! I will edit my original post.
Jul 20, 2019 at 17:47 comment added Carl Woll @sonicboom Since your function has no singularity at the origin, why are you trying to 'arc around' it?
Jul 20, 2019 at 17:26 comment added sonicboom Thanks but the contour actually has to 'arc around' 0, i.e., it has to go from $-\infty$ to $1$ without passing over zero.
Jul 20, 2019 at 14:58 history answered Carl Woll CC BY-SA 4.0