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I'm trying to calculate this integral:

Integrate [Exp[-I a *y] Exp[I*Sin[y]] Exp[-y*Sign[y]], {y, -Infinity, Infinity}] , where "a" - constant that i'll define later.

So the result of the calculation acсording to Mathematica is the same expression : Exp[-I a *y] Exp[I*Sin[y]] Exp[-y*Sign[y]].

What can i do to calculate my integral without defining my constant "a" and using NIntagrate?

Thank you in advance.

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# Integrate problem with undefined constant

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