Notation: $\mathrm{y}_l(x)$ is the spherical Bessel function of second kind.
I need to calculate the following indefinite integral: $$\int x^2\left(\mathrm{y}_l\left(x\right)\right)^2dx$$
I tried it using the differential equation itself and got no result. I have looked up the standard book of tables and DLMF to no avail. I'm looking for any suggestions to obtain a closed-form expression. Thanks in advance!
Exactly the same approach works as I gave in my answer to your previous question, except that this time the Wronskian terms vanish, so you obtain $$ \int x^2 (y_l(x))^2 \, dx = \frac{x^3}{4}(y_l''(x)y_l(x)-y_l'(x)y_l(x))+C, $$ which again can be simplified if desired.