Do the following integrals have a closed-form solution for any integer value of $m,l,k$ and $n$?

$\int^{\pi}_{0} P^{m}_{l}\left(\cos\theta\right)P^{n}_{k}\left(\cos\theta\right)\cot\theta d\theta$

$\int^{\pi}_{0} P^{m}_{l}\left(\cos\theta\right)P^{n}_{k}\left(\cos\theta\right)\frac{1}{\sin\theta} d\theta$