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I've been trying to prove the following inequality for several days:

[itex]\int_1^\infty \frac{\exp\left(-\frac{(x-1)^2}{2a^2}\right)}{x}dx > \ln(1+a)\quad \forall a>0. [/itex]

I've demonstrated by simulations that this inequality holds. I‘ve also proved that this inequality holds for large [itex]a[/itex]. But, proving [itex]\forall a[/itex] exhausted me...

Who can help? Many thanks!

Paola

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# How to prove an inequality for a definite exponential integral

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