Probability Density Function

[Trung]

I feel embarassed for asking, but is there a fast way to calculate this without using integration by parts?

\int 2e^(-2x)x^-1dx, 0 <= x < infinity

There's supposed to be some kind of trick, right?

[gel]

\int_0^\infty\frac{2e^{-2x}}{x}\,dx=\infty.

[Focus]

Sorry but how is this related to PDFs?