|
|
|
last edited 17 years ago by japp |
Edit detail for #314 Wrong answer for integrate(2*atan(x)/(1+x^2),x) revision 3 of 8
| 1 2 3 4 5 6 7 8 | ||
|
Editor: gdr
Time: 2008/05/18 13:42:27 GMT-7 |
||
| Note: | ||
added:
From gdr Sun May 18 13:42:27 -0700 2008
From: gdr
Date: Sun, 18 May 2008 13:42:27 -0700
Subject:
Message-ID: <20080518134227-0700@axiom-wiki.newsynthesis.org>
Status: fix proposed => fixed somewhere
no patch available
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