Bug in Mathematica's Integrate with PrincipalValue->True
- by Janus
It seems that Mathematica's handling of principal value integrals fails on some corner cases. Consider these two expressions (which should give the same result):
Integrate[UnitBox[x]/(x0 - x), {x, -Infinity, Infinity},
PrincipalValue -> True, Assumptions -> {x0 > 0}] /. x0 -> 1 // Simplify
Integrate[UnitBox[x]/(x0 - x) /. x0 -> 1, {x, -Infinity, Infinity},
PrincipalValue -> True]
In Mathematica 7.0.0 I get
I Pi+Log[3]
Log[3]
Has this been fixed in later versions? Does anybody have an idea for a (more or less) general workaround?