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No. These integral sines and exponentials are calculated through the sum of a series, of course, but in this specific case, it's not necessary.
Here, I even looked up a solution on Habr:
https://habrahabr.ru/post/146140/
(look from "The tale begins to unfold").
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Oh, and it can be obtained normally through the Dirichlet integral. But I've forgotten the Dirichlet integral too much to come up with this solution yesterday...