I am running Mathematica 11.1 on an Ubuntu machine and noticed the following unsavory behaviour today:
In[1] := Assuming[ Element[x,Reals], Integrate[1/(1 + y^2)*1/(y - x), {y, -Infinity, Infinity}, PrincipalValue -> True] ] Out[1] = Log[(-1)^(1/(1 + x^2)) e^(π /(I - x))] In[2] := Assuming[ Element[w,Reals], Integrate[1/(1 + y^2)*1/(y - w), {y, -Infinity, Infinity}, PrincipalValue -> True] ] Out[2] = -π w/(1+w^2)
Although the two answers are mathematically equivalent, it is not clear to me why the results are presented in different manners (and different enough that Simplify
or FullSimplify
does not reveal the latter from the former.
Clearly the answer should not depend on what symbol I use, but it does. I have obtained the same result using different kernels on the same computer. I could not reproduce the problem on Mathematica 8.0 or Mathematica 10.0 on two different Linux machines.
Is this perhaps an issue with my machine/setup? I would also like to know if others can reproduce this issue. I would also like to know if this issue persists in 11.2, if it does not I will upgrade.
Note: I believe that this is a different issue than covered here since using u
,v
, or z
gives the same problem as x
; only w
seems to work as desired.