Integral Fails to Converge

• To: mathgroup at smc.vnet.net
• Subject: [mg101782] Integral Fails to Converge
• From: Antoine Letendre <antoine.letendre at gmail.com>
• Date: Fri, 17 Jul 2009 05:02:02 -0400 (EDT)

```Hi!

I have a question regarding the Integral of a complicated function.
The program I am running is the following:

t =. ..;
a = 0.0105;
cw = 4.54 E - 10;
gammaw = 9.81 E + 3;
volume = 8.02 E - 5;
e = 2.08 E + 10;
p = 0.23;
nu = 1 E - 6;
n = 0.01;
l = 0.15;

cs = (3*(1 - (2*p)))/e;
s = l*gammaw*((n*cw) + cs);

K = 1 E - 20;
T = K*l*gammaw/nu;

alpha = \[Pi]*(a^2)*s/(volume*cw*gammaw);
beta = \[Pi]*T*t/(volume*cw*gammaw);

f1 = (((u*BesselJ[0, u]) -
2*alpha*BesselJ[1, u])^2) + (((u*BesselY[0, u]) -
2*alpha*BesselY[1, u])^2);

f = (8*alpha/(\[Pi]^2))*
Integrate[(((Exp[-beta*u*u/alpha])/(u*f1))), {u, 0, Infinity}]

Unfortunately it gives the error:
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy
after 9 recursive bisections in u near {u} = {0.000201031}. NIntegrate
obtained
7.35544*10^6+3.13215765502463540493899263106039262388603077493901288338310735176*10^-459
I and 1732.8568273226265` for the integral and error estimates.

Any suggestions would be of great help.