$$ \int_{-1}^{1} \frac{f(\xi)}{h^2 + (x-\xi)^2} d\xi = 1 $$ for $x \in [1,1]$ and $h < 1$
I went through all the relevant examples in Andrei D. Polyanin Alexander V. Manzhirov's 'Handbook of Integral Equations', but couldn't figure out a way to solve this simple looking equation to get a closed form solution. Numerical solution seems straightforward. I tried successive approximation, expanding in cosine series, etc., but that didn't help. Any tips towards the solution will be appreciated.