I need to integrate
\begin{equation}\tag{1} \int dk\, k^2 j_\ell''(kr)j_\ell''(kr') \end{equation} Using $$ j_\ell''(z)=\frac{1}{z^2}\bigg\{\big[\ell^2-\ell-z^2\big]\cdot j_\ell(z)+2z\cdot j_{\ell+1}(z)\bigg\} $$ I can rewrite the integral and split it in 9 terms. One of them is (up to a constant)
$$\int \frac{dk}{k^2}\, j_\ell(kr)j_\ell(kr') $$ which I don't know how to solve. I've tried using $j_\ell(z)=\sqrt{\frac{\pi}{2z}}\cdot J_{\ell+1/2}(z)$ and looking up the resulting integral in Watson's book, I find a horrendous expression
Is there a known solution to (1), or another way to solve it?