The roots (xi) and weights (ai) for n-point quadrature on [0,1] with the weight function ln2x can be seen by entering a value of n (1-26, 30, 35, 40, 45, 50).
The roots (ri) and weights (wi) for n-point quadrature on [0,∞) with the weight function r2 can be found from these using
ri = − R ln xi wi = R3 (ai / xi)
where R is a scale factor indicating the "extent" of the integrand. For DFT calculations, the R value should be comparable to the size of the atom.