How to go beyond $\int\ln(f(x))dx$

Question

For my current research in economics: my result depends crucially on but one integral: $$\int\ln(f(x))\,\mathrm{d}x$$ But I know very little (practically nothing) about the shape of function $f$. How can I integrate this? Is there a general form for the solution? I can provide more background if needed.

Answer 1

You could try integrating by parts:

$$\int ln(f(x))dx=\int 1\cdot ln(f(x))dx= xln(f(x))-\int x\frac{f'(x)}{f(x)}dx$$

You can then continue depending on what you know about the function f(x).