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Question: Fourier Transform of arctan(x)/x

Question:Fourier Transform of arctan(x)/x

asukumari 60 Maple
mathematica fourier fourier-transform inttrans
November 30 2017
1

This question caught my eye on Mathematics Stack Exchange forum and doesnt seem to be resolved even with Mapel 2017.3:

Please follow the question and the discussion here

The question simply is to find the Fourier Transform of arctan(x)/x and use its inverse to verify if the solution provided by Maple was consistent.

The same sequence was tested on Wolfram Mathematica, and correct result was obtained.

Experienced users on this forum please advise what could be the possible explaination for this result.

Maple test:
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