I want to find a closed-form solution to the following Fredholm integral equation of the second kind: $$ \phi(t) = 1 + \int_0^1 \frac1{1+|t-s|} \phi(s) ds, \qquad t \in [0,1]. $$
A good first step might be to split the integral into $\int_0^t$ and $\int_t^1$ to make the absolute value disappear...
Apart from that, I have not been succesful. The resolvent formalism did not take me anywhere. Neither did differentiating on both sides.
Any hint is very much appreciated!