Checking if Momentum Operator is Hermitian - Integration

[MPKU]

Homework Statement

I'm checking to see if the momentum operator is Hermitian. Griffiths has the solution worked out, I'm just not following the integration by parts.

Homework Equations

int(u dv) = uv - int(v du)

The Attempt at a Solution

I've attached an image of my work.

It seems there should be an additional 'dx' with my 'v' term, but then the 'uv' portion would have a 'dx', which wouldn't make much sense to me.

Thanks for your time.

 

[DrClaude]

If you set $u = f^*$, then
$$
\frac{du}{dx} = \frac{df^*}{dx}
$$
hence
$$
du = \frac{df^*}{dx} dx
$$