How Can I Quickly Calculate This Integral Without Integration by Parts?

Thread starter Trung
Start date Aug 9, 2008
Tags

Density Density function Function Probability Probability density Probability density function

AI Thread Summary

The integral $\int_0^\infty \frac{2e^{-2x}}{x} \, dx$ diverges to infinity, which raises questions about its relation to probability density functions (PDFs). Participants discuss the challenges of calculating the integral without resorting to integration by parts. Some suggest alternative methods or tricks that could simplify the process. The conversation highlights the importance of understanding the behavior of the integrand as $x$ approaches zero and infinity. Ultimately, the integral's divergence is a key takeaway in the discussion.

Aug 9, 2008

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?

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Aug 9, 2008

gel

<br /> \int_0^\infty\frac{2e^{-2x}}{x}\,dx=\infty.<br />

Aug 10, 2008

Focus

Sorry but how is this related to PDFs?

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