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Topic: interesting find, hard integral
Replies: 4   Last Post: Oct 14, 2017 2:47 AM

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Nasser Abbasi

Posts: 6,665
Registered: 2/7/05
interesting find, hard integral
Posted: Oct 9, 2017 1:48 AM
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fyi;

This integral is hard

Integrate[(E^(x/(2 + x^2))*(2 + 2*x + 3*x^2 - x^3 + 2*x^4))/(2*x + x^3),x]

It is Hebisch Problems #3. Maple, Rubi and Mathematica can not solve
it:

https://www.12000.org/my_notes/CAS_integration_tests/reports/rubi_4_11/test_cases/Independent_test_suites/Hebisch_Problems/resu3.htm#3

FriCAS can. But I just found out, that mathematica version 2.2
also can also solve it and it gives same answer as Fricas.

Mathematica version 2.2 is from 1993 !

Here is screen shot, side-by-side, version 2.2 and version 11.2
of Mathematica, showing 2.2 is able to solve this but not 11.2.

https://www.12000.org/tmp/hard_integral/22_vs_11_2.png

I just find this amazing and funny also and thought to share
it.

How can such an old version of Mathematica solve an
integral which a version that is 25 years later is not
able to?

I found this, as I was trying to see if I can run the
CAS integration tests on V2.2 of Mathematica.

--Nasser



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