>>>>> "Aleksas" == Aleksas Domarkas <aleksasd873 at gmail.com> writes:
Aleksas> On Thu, 31 Oct 2013 16:27:45 -0700
Aleksas> Raymond Toy <toy.raymond at gmail.com>
Aleksas> writes:
>>>>> "Martin" == Martin Kraska <kraska at fh-brandenburg.de> writes:
Aleksas> ??? Martin> Hi,
Aleksas> ??? Martin> using Maxima 5.31.2 I tried this:
Aleksas> ??? Martin> integrate(sqrt(1+cos(x)^2),x) and get nothing but the input.
Aleksas> ??? Martin> When loading abs_integrate, the result is an error:
Aleksas> ??? Martin> sign: argument cannot be imaginary; found %i
Aleksas> ??? Martin> #0:
Aleksas> ??? Martin>
Aleksas> intfudu(exp=sqrt(6*%e^-(2*%i*x)+%e^-(4*%i*x)+1)*%e^(%i*x),%voi=x)(partition.
Aleksas> ??? Martin> mac line 95)
Aleksas> ??? Martin> #1:
Aleksas> extra_integrate(q=sqrt(6*%e^-(2*%i*x)+%e^-(4*%i*x)+1)*%e^(%i*x),x=x)
Aleksas> ??? Martin> -- an error. To debug this try: debugmode(true);
Aleksas> ??? Martin> Maple gives:
Aleksas> ??? Martin> {sqrt(sin(x)^2)*EllipticE(cos(x),i)}/sin(x)
Aleksas> ??? Martin> Can this be done in Maxima?
Aleksas> As you've discovered, Maxima cannot do this integral.? Maxima
Aleksas> currently has no support for elliptic integrals.
Aleksas> I've done a little work on this, but have never finished it. It
Aleksas> definitely won't recognize this integral, but it might recognize the
Aleksas> equivalent integrate(sqrt(1+x^2)/sqrt(1-x^2),x). I didn't try it,
Aleksas> however.
Aleksas> Ray
Aleksas> Example. Compute integrate(sqrt(1+cos(x)^2),x).
Aleksas> (%i1) f:sqrt(1+cos(x)^2);
Aleksas> (%o1) sqrt(cos(x)^2+1)
Aleksas> After reading maxima documentation about elliptic integrals
Aleksas> I conclude that the answer is
Aleksas> (%i2) F:elliptic_e(x-%pi/2, -1);
Aleksas> (%o2) elliptic_e(x-%pi/2,-1)
Aleksas> Test:
Aleksas> (%i3) diff(F,x);
Aleksas> (%o3) sqrt(cos(x)^2+1)
Aleksas> Only the derivative with respect to x is known by Maxima.
Aleksas> Serious problems obtained in the calculation of the numerical values of F.
Don't leave us hanging! What serious problems did you encounter in
computing the numerical values?
Ray