Primitive of $u'' /u$

Question

There is a primitive for $$f'(x)/f(x)$$ which is $\ln(f(x))$ but is there any known primitive for $f''(x)/f(x)$ ?

Answer 1

There's isn't, in general, an elementary primitive for $f''(x)/f(x)$. Take, for example, $f=\log$. The integral $\int\frac{-1}{x^2\log(x)}\,dx$ can't be expressed in terms of elementary functions.