I have to solve the equation $$\int_{\mathbb R} \frac{f(t)}{1+(x-t)^2} dt =\frac{\sin x}{x}.$$ I tried change of variables to make the $\frac{1}{1+(x-t)^2}$ part resemble $e^{h(x)}$ so I can use the inverse Fourier transform. But I can't get it right.
Is it the right way to approach this problem?
Any help would be highly appreciated!
Thank you!