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last edited 15 years ago by japp |
Edit detail for #314 Wrong answer for integrate(2*atan(x)/(1+x^2),x) revision 4 of 8
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Editor: japp
Time: 2008/10/14 06:03:22 GMT-7 |
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added:
From japp Tue Oct 14 06:03:22 -0700 2008
From: japp
Date: Tue, 14 Oct 2008 06:03:22 -0700
Subject: From Fricas
Message-ID: <20081014060322-0700@axiom-wiki.newsynthesis.org>
http://fricas.svn.sourceforge.net/viewvc/fricas/trunk/src/algebra/gaussian.spad.pamphlet?r1=257&r2=358&view=patch
The antiderivative should be 
, however:
axiom
integrate(2*atan(x)/(1+x^2),x)
 | (1) |
Type: Union(Expression Integer,...)
axiom
D(%,x)
 | (2) |
Type: Expression Integer
axiom
D(atan(x)^2,x)
 | (3) |
Type: Expression Integer
Maybe this is related to bug #293, i.e., Axiom choosing the wrong branch of 
, or #141?
Yes, it is related to #293 --kratt6, Tue, 29 Aug 2006 04:55:37 -0500 reply
Look at
axiom
f x == 2*atan(x)+atan(2*x/(x^2-1))
Type: Void
Differentiating, we see that 
is constant
axiom
D(f x, x)
axiom
Compiling function f with type Variable x -> Expression Integer
 | (4) |
Type: Expression Integer
However, is not continuous at 1, and indeed,
axiom
numeric f(%pi)
axiom
Compiling function f with type Pi -> Expression Integer
 | (5) |
Type: Float
Drawing the function makes the situation quite clear...
Category: Aldor Library Compiler => Axiom Library Status: open => fix proposed Status: fix proposed => fixed somewhereno patch available