Re: Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg74401] Re: Integrate*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Mon, 19 Mar 2007 22:10:12 -0500 (EST)*References*: <etikok$j7r$1@smc.vnet.net>

"dimitris" <dimmechan at yahoo.com> wrote: > Hello again! > > Of course sometimes things work quite unexpectedly! > > Consider again the integral (no! I am not obsessed with it!) > > Integrate[Log[Sin[x]^2]*Tan[x], {x, 0, Pi}] > Integrate::idiv: Integral of Log[Sin[x]^2]*Tan[x] does not converge > on {x,0,Pi}. Obsessed or not, it is a curious bug, being platform dependent. You might be interested in an antiderivative, not directly obtainable from Mathematica AFAIK, which is valid over the whole real line: Letting u = Abs[Cos[x]], Integrate[Log[Sin[t]^2]*Tan[t], {t, 0, x}] is Log[2]^2 - Pi^2/3 + 2 Log[1 + u] Log[(1 + 1/u)/2] + 4 Log[Sqrt[2/(1 + u)]] Log[Sqrt[(1 - u)/2]] + 2 PolyLog[2, 1/(1 + u)] + PolyLog[2, 2 - 2/(1 + u)] + PolyLog[2, 1 - 2/(1 + u)] I'm not sure whether the result above could be simplified further or not. David W. Cantrell