Is Ei exponential integral? if so, I believe that is concave for denominator < 1 and convex for denominator > 1. Assuming L > 0, the denominator will always be >= 0, but not necessarily > 1.
And this is multiplied by the exp term and is supposedly convex? I’m not buying it, even for a single scalar X. Accordingly, I am marking this non-convex until you prove otherwise.