On p. 16 in appendix 3 in section I.2 of Quantum Field Theory in a Nutshell by Zee the integral to be evaluated is $$I = \int_{-\infty}^{+\infty}dqe^{-(1/\hbar)f(q)}.$$
Where $f(q)$ is expanded as
$$f(q) =f(a)+\frac{1}{2}f’’(a)(q-a)^{2}+O[(q-a)^{3}].$$
Then the resultant is
$$I = e^{-(1/\hbar)f(a)}(\frac{2\pi\hbar}{f’’(a)})^{\frac{1}{2}}e^{-O(\hbar^{\frac{1}{2}})}.\tag{27}$$
Where does the term $\hbar^{\frac{1}{2}} $ in the power of exponential in the resultant comes from?
