Removing extraneous factors in Einstein Action

I have an action of the form
$$\int \alpha \sqrt{g} R$$
where $\alpha$ is a field.
I want to do some kind of coordinate transformation, so that this term in the action becomes
$$\int \sqrt{g}R + \sqrt{g}(...)$$
where (...) consists of terms containing \alpha.

So basically, I want to remove $\alpha$ from the coefficient of R and move it to other terms in the lagrangian. Now, I know that this can be done! (I remember this from long ago), but for heaven's sake can't figure out how!

Can any one tell me? Just a reference would be fine.