       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.

```

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