[Maxima] try antiderivative with other CAS
raymond.toy at stericsson.com
Thu Jul 16 10:30:46 CDT 2009
Barton Willis wrote:
> If somebody with Mathematica / Axiom / ... could try:
> I would appreciate it. Wolfram | Alpha doesn't get the antiderivative
> and Maple 10 gives a huge expression involving various radicals
> (sqrt(3) and sqrt(5)) and several inverse Jacobi functions. At least
> for a naive Maple user (me), Maple isn't able to simplify the expression.
> But the antiderivative isn't all that messy. (My) function elliptic_int
> looks for antiderivatives that involve inverse_jacobi_sn. The
> ev(diff(%,x),diff, ratsimp) crazyness is due to noun/verb confusion in the
> simplification of inverse_jacobi_sn (the asin in %o221 is generated by
> a inverse_jacobi_sn expression).
> (%i220) e : ((2*x-1)*sqrt(-(x^2-x-1)*(x^2-x+1)))/((x^2-x-1)*(x^2-x+1));
> (%o220) ((2*x-1)*sqrt((-x^2+x+1)*(x^2-x+1)))/((x^2-x-1)*(x^2-x+1))
> (%i221) elliptic_int(e,x);
> (%o221) (%i*(2*x^4-4*x^3+2*x^2-2)*asin((sqrt(2)*%i*sqrt(x^2-x-1))/2))/(sqrt
FWIW, here is a different antiderivative:
I got this using my (currently broken) elliptic integral code. This
integral tickles a bug, but it gets far enough to show that the
substitution u=x-1/2 will reduce the integrand:
If we eyeball this, this is the same as -8*u/sqrt((4*u^2+3)*(5-4*u^2))
(for appropriate range of u). Then
There's another bug here, I think. The factor 4 shouldn't be there.
Substituting u=x-1/2 gives the above answer, once the factor 4 is removed.
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