Mathematica: Wolfram Alpha and Wolfram Engine produce different Laplace transforms

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Wolfram Alpha and Wolfram Engine produce different Laplace transforms
I hope you found a solution that worked for you :)
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Thanks to all those great people for their contributions!

(mathematica.stackexchange.com/users/96098/mehrshad-khansarian)Mehrshad Khansarian
(mathematica.stackexchange.com/users/7152/user64494)user64494
(mathematica.stackexchange.com/users/9362/bob-hanlon)Bob Hanlon
(mathematica.stackexchange.com/users/96098/mehrshad-khansarian)Mehrshad Khansarian
A special thanks goes out to the (https://mathematica.stackexchange.com/questions/296004/wolfram-alpha-and-wolfram-engine-produce-different-laplace-transforms)Stackexchange community

I wish you all a wonderful day! Stay safe :)

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