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Topic: can your system handle 4th-root pseudo-elliptics?
Replies: 17   Last Post: Sep 24, 2017 12:37 PM

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Posts: 1,245
Registered: 4/26/08
can your system handle 4th-root pseudo-elliptics?
Posted: Aug 28, 2017 12:09 PM
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... as promised last year (on Tue, 15 Nov 2016 23:04:20 +0100 in the
thread "FriCAS web interface failure") here are some pseudo-elliptic
integration exercises involving fourth roots. Does your favorite
integrator arrive at the elementary results?

INT((a + b*x)/((2 - x^2)*(x^2 - 1)^(1/4)), x)

INT((a + b*x)/((2 + x^2)*(1 + x^2)^(1/4)), x)

INT((3 + x^2)/((1 + x^2)*(1 + 6*x^2 + x^4)^(1/4)), x)

INT((3 - x^2)/((1 - x^2)*(1 - 6*x^2 + x^4)^(1/4)), x)

The integrals are taken from or based on papers by Euler dated to 26th
March 1777, which can be found as items E688 and E690 at the Euler
Archive <>, or on pp. 98-117 and 127-131 of
the Nova Acta Academiae Scientiarum Imperialis Petropolitanae IX (1795
for 1791).


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