MathDB

Consider a function

f:\mathbb{R}\longrightarrow\mathbb{R}

that admits bounded primitives. Prove that the function

g:\mathbb{R}\longrightarrow\mathbb{R}

defined as

f(x)=\left\{ \begin{matrix} x, & &emsp; x\le 0 \\ f(1/x)\cdot\ln x ,& &emsp; x>0 \end{matrix}\right.

admits primitives.
Florian Dumitrel

Problem Statement