integrate(log(1+(1+x**2)**0.5), x) -> incorrect result

• Subject: integrate(log(1+(1+x**2)**0.5), x) -> incorrect result
• From: Joost Witteveen
• Date: Fri, 28 Nov 2008 22:50:02 +0100

When I ask maxima to:
  integrate(log(1+(1+x**2)**0.5), x)
it comes with the answer:
      x*log((x**2+1)**0.5+1)  -  (x**2+1)**1.5 / (3*(x**2+1)+3*x+3)
but that is wrong (differentiating it again to x gives the wrong result).

I tried it with maxima 5.13.0 (from debian-testing (lenny)), and 5.10.0
(debian etch).
I attempted to build the cvs version as well, but gcl segfaults during
./configure.

I notice that if I change the expression to:
  integrate(log(1+(1+x**2)**(1/2)), x)
that now at least maxima notices it cannot integrate it.

For what it's worth, Wolfram does integrate it, and claims:

*Integrate[Log[1 + (1 + x^2)^(1/2)], x] ==*
-x + ArcSinh[x] + x*Log[1 + Sqrt[1 + x^2]]

(this seems to be correct)

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