Date: Apr 20, 2013 3:36 PM
Author: clicliclic@freenet.de
Subject: Re: An independent integration test suite


Axel Vogt schrieb:
>
> Here in Maple syntax (hopefull translated correctly, but I modified
> muliple identities). Have not yet checked all (already the first is
> not directly 'true' in Maple):
>
> Int(1/(-b^2*x^2+a^2),x) =
> 1/a/b*arctanh(b*x/a)
>


How can this be "not true" in Maple? Differentiation of the
antiderivative

DIF(1/(a*b)*ATANH(b*x/a), x)

1/((b*x + a)*(a - b*x))

leads back to the integrand. So the differentiated equation must
simplify to 'true'.

Martin.