Evaluate $\int^1_{-1} \frac{P_{l_1}^{m_1}(x)P_{l_2}^{m_2}(x)}{\sqrt{1-x^2}} dx$

Question

I wish to evaluate $\int^1_{-1} \frac{P_{l_1}^{m_1}(x)P_{l_2}^{m_2}(x)}{\sqrt{1-x^2}} dx$.

There is a neat way to show the integral is zero for certain combinations of ms and ls shown here: Integrating Associated Legendre Polynomials

However I would like to know how to get the rest!

Edit: Ah it reduces to the integral found here Integration of product of Associated Legendre Polynomial by the recurrence formula!