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## [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2

**From**: |
Vladimir Bondarenko |

**Subject**: |
[Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ? |

**Date**: |
Fri, 11 Feb 2005 16:56:14 +0200 |

Good Day,
My question is should this be interpreted as a bug or as a feature?
===> Case 1.
"When real parameters are present, the form of the integral can
depend on the signs of some expressions. Rather than query the
user or make sign assumptions, Axiom answers.
integrate(1/(x**2 + a),x)" etc
-> # integrate(log(a+z^2), z) -- understandable, a feature
However, we see also
===> Case 2.
-> integrate(log(%i+z^2), z)
+-----+ 2
+-----+ z\|- 4%i + z - %i 2
\|- 4%i log(-------------------) + 2z log(z + %i) - 4z
2
z + %i
[-------------------------------------------------------,
2
+---+
2 +---+ \|4%i
z log(z + %i) - \|4%i atan(------) - 2z]
2z
and all is OK for both of them
-> D(integrate(log(%i+z^2), z)[[1]],z)
2
log(z + %i)
-> D(integrate(log(%i+z^2), z)[[2]],z)
2
log(z + %i)
But why the user really needs 2 forms of the same answer?
So, how to classify this?
Much thanks for clarification in advance.
Best wishes,
Vladimir

**[Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**,
*Vladimir Bondarenko* **<=**
**RE: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**, *Bill Page*, `2005/02/13`
**Re: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**, *William Sit*, `2005/02/14`
**Re[2]: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**, *Vladimir Bondarenko*, `2005/02/14`
**RE: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**, *Bill Page*, `2005/02/14`
**Re: [Axiom-developer] [Q] How to classify # integrate(log(%i+z^2), z) -> 2 ?**, *William Sit*, `2005/02/15`
**[Axiom-developer] Archive file naming request**, *Camm Maguire*, `2005/02/15`
**RE: [Axiom-developer] Archive file naming request**, *Bill Page*, `2005/02/15`