Symmetry would work pretty nicely:
\int^{1}_{-1}{ln^2|x| dx} = 2\int^{1}_{0}{ln^2(x) dx} = 2 \lim_{a \rightarrow 0}{\int^{1}_{a}{ln^2(x) dx}} = dwhere d the value of the integral, or \pm \infty if it diverges.
I think you need to be specific as to how the system actually works. Is the long pole rotating clockwise while applying a force on the projectile from angle alpha to beta? If this is the situation, then you can get an equation involving F, alpha, beta, and d. You would not be able to get an...