I am trying to find analytical solution of the below integral equation (resulting from an elasticity problem) $$ \int_0^R \arcsin \left( \frac{t}{R} \right) \phi(t) \, \mathrm{d}t = \frac{2-R^2}{(1+R^2)^{5/2}} \, . $$
Here $\phi(t)$ is the unknown function and $R$ is a positive finite real number.
It would be great if someone here could provide with some useful hints/ideas that may help a bit.
Cheers
Fede