MathAction #314 Wrong answer for integrate(2*atan(x)/(1+x^2),x)

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The antiderivative should be , however:

axiom
integrate(2*atan(x)/(1+x^2),x)

Type: Union(Expression Integer,...)

axiom
D(%,x)

Type: Expression Integer

axiom
D(atan(x)^2,x)

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

Type: Expression Integer

However, is not continuous at 1, and indeed,

axiom
numeric f(%pi)

axiom

Compiling function f with type Pi -> Expression Integer

Type: Float

Drawing the function makes the situation quite clear...

fixed in FriCAS --kratt6, Thu, 20 Dec 2007 00:56:46 -0800 reply

Category: Aldor Library Compiler => Axiom Library Status: open => fix proposed

... --gdr, Sun, 18 May 2008 13:42:27 -0700 reply

Status: fix proposed => fixed somewhere

no patch available