Please show all work.

Given a wavefunction (x,t) well-defined in the real axis x(,), we want to prove that the 1D momentum operator px=idxd is Hermitian. One way to do this is via evaluating its expectation value px, and showing that it is always real, i.e. that px=px. Recall that o^=o^d, where tau() represents all space, in this case x[,], and that o^d=(o^)d. To help, it is useful to note that (x,t)2 vanishes when x. HINT: Evaluate the expectation value via integration by parts