Bessel function Integral from a physical problem

Question

$$ \int_{0}^{\infty}\frac{x\,\mathrm{I}_{0}\left(x\right) \mathrm{I}_{1}\left(x\right)\mathrm{K}_{1}^{2}\left(x\right)}{ax\,\mathrm{K}_{0}\left(x\right)\mathrm{I}_{1}\left(x\right) + 1}\,\mathrm{d}x $$

I've tried to use wolfram alpha but it said that the integral was not convergent. But physically it is supposed to converge. I have no idea how to solve this right now.

Thanks in advance.

Answer 1

Wolfram alpha seems to be correct. Maple confirms that the integrand is asymptotic to $1/(4x)$ as $x \to \infty$, and thus the integral diverges.