It goes like this:

lim[x->infinity](1 + (x + 1)/(4x^2 + 4x + 4))^(4x+1).

The solution is e, that I got with Mathematica and by myself, using a few applications of l'Hopital's rule, but the calculation is very long and tedious...

Is there any other way to solve it? Could we use the known equality lim[n->infinity](1+1/n)^n = e?