Question on PrincipalValue in Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg80672] Question on PrincipalValue in Integrate*From*: "Jung-Tsung Shen" <jushen at gmail.com>*Date*: Tue, 28 Aug 2007 06:38:57 -0400 (EDT)

A question on the "PrincipalValue" in the option of the command, Integrate: Mathematica (v5.0 Mac) gives the following command Integrate[1/(y-x), {x, -d, d}, PrincipalValue -> True] the answer If[y > 0 && y < d, I Pi - Log[d - y] + Log[d + y], Integrate[1/(-x + y), {x, -d, d}, Assumptions -> d ? y || y ? 0]] But shouldn't the first part of the answer by - Log[d - y] + Log[d + y], without the I Pi? This can be computed using the very definition of the principal value. Any comments are greatly appreciated. Thanks. JT PS. Recently I have found several verified bugs in v5.0. Maybe it's time to upgrade to v6.0?