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MathGroup Archive 1999

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Re: Tough Integral

  • To: mathgroup at
  • Subject: [mg20285] Re: Tough Integral
  • From: "Bill Bertram" <wkb at>
  • Date: Mon, 11 Oct 1999 02:19:56 -0400
  • Organization: Australian Nuclear Science and Technology Organisation
  • References: <7tp7fj$>
  • Sender: owner-wri-mathgroup at

Lawrence Walker wrote in message <7tp7fj$95g at>...
>Mathematica is able to calculate the following integral.
>For the life of me, I cannot solve this by hand.  Does any
>know or has any ideas.

Yes, I have one.

Rewrite the integral as

Integrate[ E^(-x) x^3/(1-E^(-x)),{x,0,Infinity}

Now  expand the 1/(1-E^(-x)) factor as a power series,  Sum[ E^(-k
x),{k,0,Infinity}} and integrate the result term by term. You will end up
with a sum of reciprical powers,( ie. a Zeta function) which gives you the
desired numerical result.


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