Solving the integral with Bessel function

I'm trying to solve the integral of variable x (from 0 to Inf) which is the function of variable S. I want to solve this integral and find the vector of results dependent on variable S. integral

I want to then approximate this function by polyfit (to have a function E(S))

Unfortunately, the MATBAL calculates only NaN number. It isvery important for me.. Please, help.

nu=0; int_val=zeros([255,1]);
for i=1:255
   S=i/10;
   %besselj(0,S*2)
   fun = @(x)log(abs(x-(pi/2)^2.*(-S.^2/2))).*x.*exp((x.^2+S.^2)/2).*besselj(nu,S.*x);
   int_val(i) = integral(fun,0,Inf);
end

[Torsten]

Shouldn't it be

exp(-(x^2+S^2(x))/2)

in your function definition ?

Best wishes

Torsten.