Date: Jan 12, 2013 12:50 PM
Author: clicliclic@freenet.de
Subject: Bronstein pseudoelliptic

I believe I read somewhere that Bronstein's pseudo-elliptic integral

INT(x/SQRT(x^4 + 10*x^2 - 96*x - 71), x)

= - 1/8*LN(- (x^6 + 15*x^4 - 80*x^3 + 27*x^2 - 528*x + 781)

*SQRT(x^4 + 10*x^2 - 96*x - 71)

+ x^8 + 20*x^6 - 128*x^5 + 54*x^4 - 1408*x^3 + 3124*x^2 + 10001)

<http://mathforum.org/kb/message.jspa?messageID=1562809>

could now be solved by Mathematica, but according to the Wolfram

Integrator site, this is still not the case (the integral is still done

in terms of incomplete elliptic F, incomplete elliptic Pi, and Root

objects).

<http://integrals.wolfram.com/index.jsp>

A problem with the above elementary antiderivative is a jump near x =

3.531 (where the radicand is negative). Can the logarithm argument be

factored perhaps?

Martin.