You need to provide us the details of your optimization problem formulation. If there are three additive terms in the objective function, each of which are representable in CVX, then the sum of these terms will also be representable in CVX.
The link you provided shows how to formulate the problem in that link in CVX. As for your additional term, alph*exp(x/sigma), you need to tell us which of alph, x, and sigma are optimization (decision) variables, and which are input data. If x is the only optimization variable among these three, you can enter that term in CVX exactly as you have written it.
The first thing you must do is show that your optimization problem is convex. Please read Why isn't CVX accepting my model? READ THIS FIRST! and http://cvxr.com/cvx/doc/ .