integrate(log(1+(1+x**2)**0.5), x) -> incorrect result
Subject: integrate(log(1+(1+x**2)**0.5), x) -> incorrect result
From: Raymond Toy
Date: Sat, 29 Nov 2008 10:27:37 -0500
Stavros Macrakis wrote:
> On Fri, Nov 28, 2008 at 10:10 PM, Raymond Toy <toy.raymond at gmail.com
> <mailto:toy.raymond at gmail.com>> wrote:
>
> > integrate(log(1+(1+x**2)**(1/2)), x)
>
> Maxima can't compute the integral completely by itself, unfortunately,
> but it does get close:
>
>
FWIW, the original integral with 0.5 instead of 1/2 fails in rischint.
In both cases we get to the point of trying to integrate
x^2/(1+x^2+(1+x^2)^(1/2)). When the power is 1/2, rischint returns the
noun form. But when the power is 0.5, rischint returns the incorrect
answer.
I don't understand the rischint code, so I don't know why it produces
the wrong answer.
One obvious workaround is to rationalize the expression before calling
rischint so that it never has to deal with float numbers.
Ray