Re: A wrong definite integral in 5.0? (2nd response)

*To*: mathgroup at smc.vnet.net*Subject*: [mg77280] Re: A wrong definite integral in 5.0? (2nd response)*From*: dimitris <dimmechan at yahoo.com>*Date*: Wed, 6 Jun 2007 07:11:49 -0400 (EDT)*References*: <f43hau$301$1@smc.vnet.net>

As a second workaround i suggest you trying in Mathamatica 5.0 the following In[153]:= Integrate[Exp[(-x)*s]*Log[1 - 4*x*(1 - x)], {x, 0, 1}, GenerateConditions -> False] Out[153]= -((4*SinhIntegral[s/2])/(E^(s/2)*s)) In[154]:= Limit[%, s -> 0] Out[154]= -2 Does it work? Dimitris / bolud-el-kotur : > 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.