About the inverse of a function $f$ with integral I'm having a lot of trouble finding the inverse of this function, I'm not quite sure even where to begin with..
$$f(x) = x\sqrt{1-x^2} + 2\int_0^1 \sqrt{1-t^2} \, dt$$
Dom is $\mathbb R$.
Could you guys offer help?

The integral is a constant, so I will denote it with $C$. You have
$$y=x\sqrt{1-x^2}+C$$
$$y-C=x\sqrt{1-x^2}$$
$$(y-C)^2=x^2*(1-x^2)$$
$$(y-C)^2=x^2-x^4$$
Substitue $u=x^2$.
$$u^2-u+(y-C)^2=0$$
From there, use the quadratic formula to get your answer, and then fix the domain and range so that everything is real, unless you want it to be complex.
