I'm feeling a little lost in trying to solve equations of the form: $$f(x)+\int_a^b\phi(x,t)\mathrm{d}t=0$$ Where the integral in the LHS is non-elementary, and the variable $x$ is the unknown.
If the integral is elementary, then, the only solving method i'm aware of is taking an antiderivative $\Phi(x,t)$ for the integral and solving for $x$ in the equation: $$f(x)+\Phi(x,b)-\Phi(x,a)=0$$ But, this is not the case. That means that the previous method is not an option. Is there a general procedure to solve this kind of equations? If there isn't, does this means that the equation is "algebraically" unsolvable?