Hello gurus,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How to prove an inequality for a definite exponential integral

Loading...

Similar Threads - prove inequality definite | Date |
---|---|

Proof sin x < x for all x>0. | Oct 11, 2015 |

Help proving triangle inequality for metric spaces | Sep 12, 2015 |

Proving inequality | Mar 26, 2011 |

I'm trying to figure out how to prove this inequality | Jan 27, 2011 |

How do you prove this consequence of the triangle inequality? | Apr 16, 2009 |

**Physics Forums - The Fusion of Science and Community**