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Topic: An independent integration test suite
Replies: 128   Last Post: Dec 8, 2013 3:21 PM

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Axel Vogt

Posts: 1,038
Registered: 5/5/07
Re: An independent integration test suite
Posted: Apr 21, 2013 5:48 AM
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Ok, for this 86 given integrals (translated to Maple syntax) Maple 17 solves all,
BUT ONE, Int(exp(1/2*x)/(exp(x)-1)^(1/2),x) = 2*ln((exp(x)-1)^(1/2)+exp(1/2*x)).

That can be done manually:

Int(exp(1/2*x)/(exp(x)-1)^(1/2),x);
Change(%, exp(1/2*x) = y, y);
value(%);
subs(y = exp(1/2*x), %); # re-substitute
combine(%); # re-write, giving the asserted


For the remaining 85 solutions it can automatically prove that lhs = rhs after
differentiation w.r.t. x and it fails for no. 50, 52, 53:

#Int(x/(a^4-x^4)^(1/2),x)
1/2*arctan(x^2/(a^4-x^4)^(1/2)) =
1/2*arcsin(x^2/a^2),

#Int(1/(x*(a^2-x^2)^(1/2)),x)
-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2-x^2)^(1/2))/x) =
-1/a*arctanh((a^2-x^2)^(1/2)/a),

#Int(1/(x*(a^2+x^2)^(1/2)),x)
-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2+x^2)^(1/2))/x) =
-1/a*arctanh(a/(a^2+x^2)^(1/2))

Assuming a<>0 resolves the last two ones.


For the first one I think that is false for a= exp(I*Pi/4),
as already said in a previous post (20.04.2013)


Date Subject Author
2/24/13
Read An independent integration test suite
clicliclic@freenet.de
3/19/13
Read where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/21/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/22/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
3/26/13
Read Re: where the air gets thin for Axiom & Co.
Waldek Hebisch
3/26/13
Read Re: where the air gets thin for Axiom & Co.
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Nasser Abbasi
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Rouben Rostamian
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
Axel Vogt
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/21/13
Read Re: An independent integration test suite
Waldek Hebisch
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/22/13
Read Re: An independent integration test suite
Axel Vogt
4/22/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/23/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Waldek Hebisch
4/24/13
Read Re: An independent integration test suite
Richard Fateman
4/24/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Richard Fateman
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Axel Vogt
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/25/13
Read Re: An independent integration test suite
Waldek Hebisch
4/25/13
Read Re: An independent integration test suite
Peter Pein
4/25/13
Read Re: An independent integration test suite
Nasser Abbasi
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Peter Pein
4/26/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/26/13
Read Re: An independent integration test suite
Richard Fateman
4/27/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/27/13
Read Re: An independent integration test suite
Richard Fateman
6/30/13
Read Re: An independent integration test suite
clicliclic@freenet.de
6/30/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite / Chap 3
clicliclic@freenet.de
7/1/13
Read Re: An independent integration test suite / Chap 3
Axel Vogt
7/1/13
Read Re: An independent integration test suite
Waldek Hebisch
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/2/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/4/13
Read Re: An independent integration test suite
Nasser Abbasi
7/5/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/5/13
Read Re: An independent integration test suite
Nasser Abbasi
7/9/13
Read Re: An independent integration test suite
clicliclic@freenet.de
7/10/13
Read Re: An independent integration test suite
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite/ Klerer?
Richard Fateman
7/10/13
Read Re: An independent integration test suite/ Klerer?
Nasser Abbasi
7/10/13
Read Re: An independent integration test suite
clicliclic@freenet.de
8/6/13
Read Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/15/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/21/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/24/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/30/13
Read Re: Rubi 4.1 and the Timofeev test suite
daly@axiom-developer.org
9/22/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/25/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/26/13
Read The Timofeev symbolic integration test suite
Albert D. Rich
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
9/26/13
Read Re: Rubi 4.1 and the Timofeev test suite
Albert D. Rich
9/29/13
Read Re: Rubi 4.1 and the Timofeev test suite
clicliclic@freenet.de
10/1/13
Read The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/1/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/5/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
10/10/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
10/11/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/6/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/12/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/13/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/21/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/22/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/14/13
Read Re: The A. F. Timofeev symbolic integration test suite
Albert D. Rich
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/15/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
11/16/13
Read Re: The A. F. Timofeev symbolic integration test suite
Nasser Abbasi
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
did
11/7/13
Read Re: The A. F. Timofeev symbolic integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Richard Fateman
4/21/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Axel Vogt
4/20/13
Read Re: An independent integration test suite
clicliclic@freenet.de
4/20/13
Read Re: An independent integration test suite
Waldek Hebisch
4/21/13
Read Re: An independent integration test suite
G. A. Edgar
12/8/13
Read Re: An independent integration test suite
clicliclic@freenet.de
10/5/13
Read Re: An independent integration test suite
Albert D. Rich
10/6/13
Read Re: An independent integration test suite
clicliclic@freenet.de

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