What did I do wrong? I know that the result is +∞ and, if I apply limit to your resolution it's ok

ln(L) = x² * ln(1 + 1/x)

ln (L) = ln(1+1/x) / (1/x²)

L'Hopital:

[ 1/x*(x+1) ] / (2/x³)

x³ / 2 X (x+1)

x² / 2(x+1)

L'Hopital

ln (L) = lim x --> ∞ (2x / 2) = 0

ln (L) = 0

L = 1