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Find the two integrals:
[tex]\int_0^{\infty}\frac{e^{-\alpha x^2}}{x^2+1}\sin(\alpha x) \, dx [/tex]
[tex]\int_0^{\infty}e^{-\beta^2t}\cos(\beta x) \, d\beta [/tex]
Any hint?
[tex]\int_0^{\infty}\frac{e^{-\alpha x^2}}{x^2+1}\sin(\alpha x) \, dx [/tex]
[tex]\int_0^{\infty}e^{-\beta^2t}\cos(\beta x) \, d\beta [/tex]
Any hint?