Re: Calculation of a not so simple integral

• To: mathgroup at smc.vnet.net
• Subject: [mg131216] Re: Calculation of a not so simple integral
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Mon, 17 Jun 2013 06:31:32 -0400 (EDT)
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```(*Partial Fractions decomposition,  Fourier Integrals

The problem diagnostics:

Calculate

Integrate[ Sin[x/2]^2 / x^2 / (x^2-4*Pi^2 )^2 / (x^2 + a^2)^2 ,
{x,-oo,oo}, Assumptions-> a>0]

The integrand is nonnegative, has no poles on the real line and decays
rapidly  ~ x^-10 as x->+-oo

Hi, Roland,

I checked your expression, it has a pole on the x axis. Check this

Sin[x/2]^2 / x^2 / (x^2-4*Pi^2 )^2 / (x^2 + a^2)^2//StandardForm

Could it be the case, that you have just written it down in a wrong way?

Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
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L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
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e-mail: alexei.boulbitch at iee.lu

```

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