# Convergent of improper integral

Let $$f in C^1(0,infty)$$ be an increasing function with $$f(0)>0$$, suppose $$int_0^infty frac{1}{f(x)+f'(x)} < infty$$, prove that $$int_0^infty frac{1}{f(x)} < infty$$.

I find it weird since the behaviour of $$f’$$ is random, so I don’t know how to control $$f$$ in terms of $$f+f’$$.