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

[Vladimir Bondarenko]

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