Another challenging integral
- Tolaso J Kos
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Another challenging integral
Let $\Omega$ denote the unique real root of the equation $xe^x=1$. Prove that:
$$\int_{-\infty}^{\infty} \frac{{\rm d}x}{(e^x-x)^2+\pi^2}= \frac{1}{1+\Omega}$$
$$\int_{-\infty}^{\infty} \frac{{\rm d}x}{(e^x-x)^2+\pi^2}= \frac{1}{1+\Omega}$$
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Re: Another challenging integral
here http://zerocollar.blogspot.cl/2014/08/a ... stant.html" onclick="window.open(this.href);return false;Tolaso J Kos wrote:Let $\Omega$ denote the unique real root of the equation $xe^x=1$. Prove that:
$$\int_{-\infty}^{\infty} \frac{{\rm d}x}{(e^x-x)^2+\pi^2}= \frac{1}{1+\Omega}$$
Civil Engineer
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