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I'll like to know the probability density function for one of the x or y axis, given that there is an exponential decay of a material in two-dimensional space. So, that means I have to marginalize, say y and keep x, but I couldn't solve the integration. I even tried with Mathematica and Matlab. Mathematica couldn't solve it. Matlab gives a Bessel function when x == 1, but when x != 1, it couldn't solve it. Please help.
[tex] PDF(x) = \int e^{-r} \, dy = \int e^{-\sqrt{x^2+y^2}} \, dy [/tex]
[tex] PDF(x) = \int e^{-r} \, dy = \int e^{-\sqrt{x^2+y^2}} \, dy [/tex]