Raymond,
thanks for the response. Perhaps, abs_integrate could provide a more
specific error message, but that is perhaps just nice to have and may be
difficult to do.
Martin
> Message: 4
> Date: Thu, 31 Oct 2013 16:27:45 -0700
> From: Raymond Toy <toy.raymond at gmail.com>
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] integrate(sqrt(1+cos(x)^2),x)
> Message-ID: <wvmi1u31ggwe.fsf at rtoy2.mtv.corp.google.com>
> Content-Type: text/plain; charset=us-ascii
>
> >>>>> "Martin" == Martin Kraska <kraska at fh-brandenburg.de> writes:
>
> Martin> Hi,
> Martin> using Maxima 5.31.2 I tried this:
>
> Martin> integrate(sqrt(1+cos(x)^2),x) and get nothing but the input.
>
> Martin> When loading abs_integrate, the result is an error:
>
> Martin> sign: argument cannot be imaginary; found %i
> Martin> #0:
> Martin> intfudu(exp=sqrt(6*%e^-(2*%i*x)+%e^-
> (4*%i*x)+1)*%e^(%i*x),%voi=x)(partition.
> Martin> mac line 95)
> Martin> #1: extra_integrate(q=sqrt(6*%e^-(2*%i*x)+%e^-
> (4*%i*x)+1)*%e^(%i*x),x=x)
> Martin> -- an error. To debug this try: debugmode(true);
>
> Martin> Maple gives:
>
> Martin> {sqrt(sin(x)^2)*EllipticE(cos(x),i)}/sin(x)
>
> Martin> Can this be done in Maxima?
>
> As you've discovered, Maxima cannot do this integral. Maxima
> currently has no support for elliptic integrals.
>
> I've done a little work on this, but have never finished it. It
> definitely won't recognize this integral, but it might recognize the
> equivalent integrate(sqrt(1+x^2)/sqrt(1-x^2),x). I didn't try it,
> however.
>
> Ray