Date: Jan 21, 2013 1:55 PM
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


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.