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Find the coefficients A(ω) and B(ω) in the Fourier integral of the function f(x) = e^...

Find the coefficients A(ω) and B(ω) in the Fourier integral of the function f(x) = e^ −3x if x > 0 and f(x) = 0 if x < 0 .

Full working please no short cuts, I want to see the full integration by parts.

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