Find the fourier cosine transform of e^-(a^2x^2)।Hence prove that e^-(x^2/2) is self reciprocal

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Find the Fourier cosine transform of e^(-x²/2). Hence find Fourier transform of x e^(-x²/2). Find the Fourier cosine transform of e^(-x²/2). Hence find Fourier transform of x e^(-x²/2).
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