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I wish to solve the following integral equation, preferably analytically, and find $\int_{-l}^l f(x) dx$. If analytical solution is too complicated, any suggestion for the computational method?

$A_0+\int_{-l}^l \frac{f(x')}{x-x'} dx'+\int_{-l}^l \frac{f(x')(x-x')}{\left(x-x'\right)^2+y_0^2} dx'=0$

PS: When $y_0=0$, the above equation can be solved using the Hilbert transform:

$f(x)=\frac{A_0}{2\pi}\frac{x}{\sqrt{l^2-x^2}}$

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