infinite Integration of hyperbolic function

Dear guys,

I'm going to calculate conductivity of graphene. so I forced to calculate an infinite integral containing hyperbolic sine and cosine functions . I wrote a matlab code to do that, But it diverged. would you please check my matlab code, and give me your advices to correct it's errors.

my m-file has been attached.

Answer 1

[Walter Roberson]

    y5=@(x)(4*hh.^2-4.*(x.^2));
    y6=@(x)y4(x)./y5(x);

You have a division by a constant minus 4*x^2 . But that can pass through 0 -- and does at 9.939e-21 . That gives you an unremovable discontinuity leading to undefined integral.

... And that is not even counting the fact that you are dealing with huge trigh expressions that overflow to any practical infinity by the time of x = 1.