\( \int_{0}^{\infty}{e^{-x}\ln\bigl({\ln\bigl({e^x+\sqrt{e^{2x}-1}\,}\bigr)}\bigr) \;dx}\)

Calculus (Integrals, Series)
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Tolaso J Kos
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\( \int_{0}^{\infty}{e^{-x}\ln\bigl({\ln\bigl({e^x+\sqrt{e^{2x}-1}\,}\bigr)}\bigr) \;dx}\)

#1

Post by Tolaso J Kos »

Evaluate the following integral :

$$ \displaystyle\int_{0}^{\infty}{e^{-x}\ln\bigl({\ln\bigl({e^x+\sqrt{e^{2x}-1}\,}\bigr)}\bigr) \;{\rm d}x}$$
Imagination is much more important than knowledge.
whitexlotus
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Re: \( \int_{0}^{\infty}{e^{-x}\ln\bigl({\ln\bigl({e^x+\sqrt{e^{2x}-1}\,}\bigr)}\bigr) \;dx}\)

#2

Post by whitexlotus »

Tolaso J Kos wrote:Evaluate the following integral :

$$ \displaystyle\int_{0}^{\infty}{e^{-x}\ln\bigl({\ln\bigl({e^x+\sqrt{e^{2x}-1}\,}\bigr)}\bigr) \;{\rm d}x}$$
Here http://mathimatikoi.org/forum/viewtopic ... 2161#p2161" onclick="window.open(this.href);return false;
Regards
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