Another challenging integral

Calculus (Integrals, Series)
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Tolaso J Kos
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Another challenging integral

#1

Post by Tolaso J Kos »

Let $\Omega$ denote the unique real root of the equation $xe^x=1$. Prove that:

$$\int_{-\infty}^{\infty} \frac{{\rm d}x}{(e^x-x)^2+\pi^2}= \frac{1}{1+\Omega}$$
Imagination is much more important than knowledge.
whitexlotus
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Re: Another challenging integral

#2

Post by whitexlotus »

Tolaso J Kos wrote:Let $\Omega$ denote the unique real root of the equation $xe^x=1$. Prove that:

$$\int_{-\infty}^{\infty} \frac{{\rm d}x}{(e^x-x)^2+\pi^2}= \frac{1}{1+\Omega}$$
here http://zerocollar.blogspot.cl/2014/08/a ... stant.html" onclick="window.open(this.href);return false;
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