I am looking for a way to rewrite the following equation into an integral for a general distribution of the r.v. $X$:
E[$\min\{\max(0;q_1 - X) + q_2; \alpha X \}$]
where $q_1, q_2$ and $\alpha$ are constants. Eventually I want to take the derivative of this expectation w.r.t $q_2$. Can anyone help?