I was reading about the derivation of Ehrenfest's theorem in this website when I came across this step:
Substituting from Schrödinger's equation (137) and simplifying, we obtain $$\frac{d\langle p\rangle}{dt}=\int_{-\infty}^{\infty}\left[-\frac{\hbar^2}{2m}\frac{\partial}{\partial x}\left(\frac{\partial\psi^*}{\partial x}\frac{\partial\psi}{\partial x}\right)+V(x)\frac{\partial|\psi|^2}{\partial x}\right]dx=\int_{-\infty}^{\infty}V(x)\frac{\partial|\psi|^2}{\partial x}dx$$
What I cannot understand is how the first term $$\frac{\hbar^2}{2m} \frac{d\psi^*}{dt} \frac{d\psi}{dx}$$ between the limits $x=\infty$ and $x=-\infty$ reduces to zero. I know $\psi$ and $\psi^*$ go to $0$ as $x$ goes to infinity but why does this term reduce to zero?
