Contour integration along a branch cut (example three)

In this video we will compute a real integral which is very similar to the one of the second example. Only a single minus sign is different; this cause a big difference though, because now the singularity is on the positive real axis (which is part of our contour). So we will see a pretty tricky contour integration, combining a branch cut and a singularity on the axis.

[marierosetonguino]

Your videos are amazing and super helpful! Thank you!

[Number_Cruncher]

I've heard a few times that the branch cut location can be chosen at will. Now I understand, what it means.

[OleJoe]

For this example, could you have changed the principle branch to go along the non-positive real axis? Then you could avoid the singularity.