integrate(sqrt(1+cos(x)^2),x)

>>>>> "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