lim(x->-inf) (e^x)[ln(|x|) + 3x]
lim(x->-inf) exp(x [ln(|x|)+3x])
The first of these goes to 0, as e^x decreases faster than |x|^k for
and real k as x -> -inf.
The second of these goes to +inf, as for large |x| x (ln(|x|+3x)
behaves like x^2.
If need be all of this can be made rigourous.