![Integral of Inverse Exponential Logarithmic Function from Zero to Infinity](https://writelatex.s3.amazonaws.com/published_ver/11155.jpeg?X-Amz-Expires=14400&X-Amz-Date=20240727T123414Z&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAWJBOALPNFPV7PVH5/20240727/us-east-1/s3/aws4_request&X-Amz-SignedHeaders=host&X-Amz-Signature=b5f64f0c9ddf602c818f0a7d8c36c1923ed59bd54e5c41c569c0d51b75cc84a3)
Integral of Inverse Exponential Logarithmic Function from Zero to Infinity
Author
Ivan V. Morozov
Last Updated
5 years ago
License
Creative Commons CC BY 4.0
Abstract
A proof of an integral over the interval from 0 to infinity of the function \(\frac{1}{x^{\ln x}}\) that I have derived.
![Integral of Inverse Exponential Logarithmic Function from Zero to Infinity](https://writelatex.s3.amazonaws.com/published_ver/11155.jpeg?X-Amz-Expires=14400&X-Amz-Date=20240727T123414Z&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAWJBOALPNFPV7PVH5/20240727/us-east-1/s3/aws4_request&X-Amz-SignedHeaders=host&X-Amz-Signature=b5f64f0c9ddf602c818f0a7d8c36c1923ed59bd54e5c41c569c0d51b75cc84a3)