Integration Bug

*To*: mathgroup at smc.vnet.net*Subject*: [mg65236] Integration Bug*From*: "Chris H. Fleming" <chris_h_fleming at yahoo.com>*Date*: Sun, 19 Mar 2006 03:19:14 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I am finding some weird bugs when Mathematica integrates EXP*TRIG/Polynomial to infinity. $Assumptions = {0 < t, 0 < Ï?, 0 < Î³< Î©}; Ï?1 = +Î© + i Î³; Ï?2 = +Î© - i Î³; Ï?3 = -Î© + i Î³; Ï?4 = -Î© - i Î³; this integral is correct Integrate[Ï? Cos[Ï? t] / ((Ï?-Ï?1)(Ï?-Ï?1)(Ï?-Ï?1)(Ï?-Ï?1)),{Ï?,0,Infinity}] //FullSimplify Although the answer it gives is correct, I want answers in Ei form and not Ci and Si so I substituted Cos[x] for 1/2(Exp[i x]+Exp[-i x]) Integrate[Ï? (Exp[i Ï? t]+Exp[-i Ï? t])/2 / ((Ï?-Ï?1)(Ï?-Ï?1)(Ï?-Ï?1)(Ï?-Ï?1)),{Ï?,0,Infinity}] //FullSimplify and this answer is in the form of Ei, but it is completely wrong similar things happen with other integrals of this kind. Fortunately I know how to do these by hand.