Integral of associated Legendre Function

[rpm2011]

I need to evaluate the following integral:
[tex]\int_0^{\pi} \lleft(\frac{P_n^1}{\sin\theta} \frac{d P_l^1}{d\theta}\right)\, \sin\theta\, d\theta [tex]

This integral, I think, has a closed form expression. Itarises in elastic wave scattrering. I am an engineer and do not have suficient background to do the integration from first principles. I looked at several books in mathemtical physics, and also many handbooks. This integral is however not listed. I will highly appreciate your help.

[LCKurtz]

I need to evaluate the following integral:
\int_0^{\pi} \left(\frac{P_n^1}{\sin\theta} \frac{d P_l^1}{d\theta}\right)\, \sin\theta\, d\theta



I don't know the answer but fixed your \LaTeX for you.