On Thu, 31 Oct 2013 16:27:45 -0700
Raymond Toy <toy.raymond at gmail.com>
writes:
>>>>> "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
Example. Compute integrate(sqrt(1+cos(x)^2),x).
(%i1) f:sqrt(1+cos(x)^2);
(%o1) sqrt(cos(x)^2+1)
After reading maxima documentation about elliptic integrals
I conclude that the answer is
(%i2) F:elliptic_e(x-%pi/2, -1);
(%o2) elliptic_e(x-%pi/2,-1)
Test:
(%i3) diff(F,x);
(%o3) sqrt(cos(x)^2+1)
Only the derivative with respect to x is known by Maxima.
Serious problems obtained in the calculation of the numerical values of F.
best
Aleksas D