A wrong definite integral in 5.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg77201] A wrong definite integral in 5.0?*From*: bolud-el-kotur <ke8eqet at hotmail.com>*Date*: Tue, 5 Jun 2007 06:56:05 -0400 (EDT)

I get this result in version 5.0, >Integrate[Log[1 - 4 x(1 - x)], {x, 0, 1}] >-2 + I Pi and the same thing if I "declare" the singularity with {x,0,1/2,1}. Another way to look at the problem is computing, >Integrate[Log[1 - 4 x(1 - x)], {x, 0, 1/2}] >-1 and >Integrate[Log[1 - 4 x(1 - x)], {x, 1/2, 1}] >-1 + I Pi Since the integrand is symmetric about x=1/2, the result should have been the same one (-1) in both cases, and the integral over [0,1] should yield -2. A numerical approach, >NIntegrate[Log[1 - 4 x(1 - x)], {x, 0, 1/2, 1}, MaxRecursion -> 100, SingularityDepth -> 20] >-1.9999997086422834` gives the correct result, within the numerical accuracy required.