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NIntegrate about singular point

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126100] NIntegrate about singular point
  • From: bowlderster <bowlderster at gmail.com>
  • Date: Tue, 17 Apr 2012 06:04:12 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello, all.
I am dealing with an integral as following

h = 1
m = 1
n = 1
t = 1
k = 4.0269
kk = 4.0284
Plot[x^(m + n - 1)/(x*Sinh[x*h] -
     kk*Cosh[x*h])*((x +
       kk)*((-1)^(m + n)*Exp[x*(2.*(-0.2) + h)] - ((-1)^m + (-1)^n)*
        Exp[-x*h]) + (x - kk)*Exp[-x*(2.*(-0.2) + h)]), {x, 0, 40}]
NIntegrate[
 x^(m + n - 1)/(x*Sinh[x*h] -
     kk*Cosh[x*h])*((x +
       kk)*((-1)^(m + n)*Exp[x*(2.*(-0.2) + h)] - ((-1)^m + (-1)^n)*
        Exp[-x*h]) + (x - kk)*Exp[-x*(2.*(-0.2) + h)]), {x, 0,
  Infinity}]

It has a singular point when the denominator is zero.
At begining, I try to solve it in another system, yet with Nan result.

It is the first time for me to use Mathematica.
Can it solve the integral with singular point?

Thanks for your help



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