Given $r,a,\lambda\in\mathbb{R}$, $r<a$, how can I find an approximate solution for the following definite integral?
$$ \int_0^\infty J_0 (\lambda r)J_1(\lambda a)\frac{1}{\sqrt{n+\lambda^2 }}\,d\lambda $$
$J_0,J_1$ are Bessel function of first kind, $0$th and $1$st order, respectively. $n$ is an imaginary parameter ($i\omega/\alpha$ where $\omega$ is angular frequency and $\alpha$ is thermal diffusivity) and cannot be considered small. $\lambda$ is the Fourier transform variable, $r$ is the radial coordinate and $a$ is a constant and can be considered small.