energy/power signals
Write the energy integral for the second signal in the same way you did for the first.

You'll see that it is a power signal too, since its energy is infinite:

$$
E_2 = \int_{-\infty}^{+\infty}{|x_2(t)|^2}dt = \int_{-\infty}^{+\infty}dt
= \lim_{T \,\to\, +\infty} \int_{-T/2}^{T/2}dt= +\infty
$$