Date: Jan 21, 2013 1:55 PM
Author: clicliclic@freenet.de
Subject: A bug in Reduce package 'algint'?


Wanting to refresh my knowledge of the capabilties of the Reduce algebra
system, I have recently browsed the website. The system comes with the
'algint' package by J. Davenport which boosts the integrator
capabilities for algebraic functions. The package documentation

  <http://www.reduce-algebra.com/docs/algint.pdf>

introduces the example integrand sqrt(sqrt(a^2 + x^2) + x)/x. A correct
antiderivative for this is 

  2*(sqrt(sqrt(a^2 + x^2) + x)
   - sqrt(a)*atanh(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a))
   - sqrt(a)*atan(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a)))

The antiderivative printed in the documentation, however, is either very
wrong or garbled beyond recognition.

Martin.