(a)[5]
Determine $f'(x)$ and hence determine the exact coordinates of the stationary point on the curve with equation $y = f(x)$.
(b)[9]
Make the substitution $u = e^x$ and use partial fractions to determine the exact value of $\int_{\ln 3}^{\ln 5} f(x)\,dx$. Present your answer as $\ln a$, where $a$ is a rational number in simplest form.