Mathematica: Same integral giving different results

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Same integral giving different results
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(mathematica.stackexchange.com/users/44995/sined)sined
(mathematica.stackexchange.com/users/62063/a-kato)A. Kato
(mathematica.stackexchange.com/users/22158/louisb)LouisB
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integral-equations special-functions integral-transforms calculus-and-analysis




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