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Bronstein pseudoelliptic
Posted:
Jan 12, 2013 12:50 PM


I believe I read somewhere that Bronstein's pseudoelliptic 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.



