Problem 1--simplified

[Victor Ivrii]

Calvin: 1) errors with the sign in denominator 2) Please don't upload pdfs as they are not displayed by Forum (so one needs to download them) 3) TeX advice: too long lines (not nice to read)


Everybody: I did not ask you to take all integrals. Instead after you found F.T. of $e^{-\alpha |x|}$ (say $G(\omega)$) you recalling properties of F.T understand that F.t. of $e^{-\alpha |x|}e^{\pm i\beta x}$ are  $G(\omega \mp \beta)$ and then F.T. of  $e^{-\alpha |x|}\cos(\beta x)$ and $e^{-\alpha |x|}\sin(\beta x)$ are $\frac{1}{2}[ G(\omega - \beta)+G(\omega + \beta)]$ and $\frac{1}{2i}[ G(\omega - \beta)-G(\omega + \beta)]$ respectively

[Victor Ivrii]

Calvin, first of all not "edited" but "converted" to png. Now why your png is rather invisible? The answer is simple: you generated pdf via TeX and therefore it has not a white but a transparent background.

Actually all graphics I generated via LaTeX with pgf package but I always put \pagestyle{empty}, then apply pdfcrop to the generated pdf,  and then convert by ImageMagick to png which inserts white background.