Knowing that the Schrödinger Equation is:

$$i\hbar\frac{\partial\Psi}{\partial t} = -\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi$$

The change of momentum in function of time is:

$$ \frac{d\langle p \rangle}{dt} = -i\hbar \int\_{-\infty}^{\infty} \frac{\partial}{\partial t} \Psi^\* \frac{ \partial \Psi}{ \partial x} dx$$

I got the expression for $\frac{\partial}{\partial t} \Psi^\* \frac{ \partial \Psi}{ \partial x}$ :

$$\frac{\partial}{\partial t} \Psi^\* \frac{ \partial \Psi}{ \partial x} = \frac{i\hbar}{2m}(\Psi^\*\frac{\partial^3 \Psi}{\partial^2x^3} - \frac{\partial^2 \Psi^\*}{\partial x^2} \frac{\partial \Psi}{\partial x}) - \frac{i}{\hbar} |\Psi|^2 \frac{\partial V}{\partial x} $$

The next step is to integrate this expression. Concretely, I am struggling to integrate this part:

$$-\frac{\partial^2 \Psi^\*}{\partial x^2} \frac{\partial \Psi}{\partial x}$$ 

I thought about integrating by parts as follows:

$$-\int \frac{\partial^2 \Psi^\*}{\partial x^2} \frac{\partial \Psi}{\partial x} = -\frac{\partial^2 \Psi^\*}{\partial x^2}\Psi + \Psi\int \frac {\partial^3 \Psi^\*}{\partial x^3} dx ...$$

But I did not get the equality.

May you help me out?