Solving a Integral

• To: mathgroup at smc.vnet.net
• Subject: [mg78043] Solving a Integral
• From: ehrnsperger.b at pg.com
• Date: Thu, 21 Jun 2007 06:03:03 -0400 (EDT)

```I need help in solving the following integral:

Integral = 1/(beta^alpha* Gamma[alpha]) *
Integrate[x^(alpha-1)*Exp[-x/beta]/(1+Exp[-a*x-b]),{x,0, infinity},
Assumptions: (alpha> 0)||(beta > 0)||(a > 0)||(b <0)]

The Integral is approximately 1/(beta^alpha* Gamma[alpha])
*1/(1+Exp[-a*alpha*beta-b]) + Order[alpha*beta^2]

However, I would like to have an exact analytical solution, and I am
failing to convince Mathematica to give me the solution. Is there a way to
ask Mathematica to give the solution as a series expansion of my
approximate solution?

Thanks so much for your help,

Bruno

Dr. Bruno Ehrnsperger
Principal Scientist

Procter & Gamble Service GmbH
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Germany

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```

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