Why has only the Cauchy Residue Theorem used for one of the solutions whilst both contour integration and CRT used in the other?

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In the solutions to the following answers only CRT has been used for B7 whilst both CRT and contour integration has been used for B6. The question is the same so I am unsure why the solutions have a varying method to find k(x,y). I suspect it might have to do with the hints given at the bottom of each question but even then for B6 it gives that hint but also requires CRT to be used since the hint would be useful for contour integration only.

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