Question 49
Let $f:(0 ;+\infty) \rightarrow \mathbb{R}$ be a continuous function such that $(x+1) f(x)+\frac{1}{x^{3}} f\left(\frac{1}{x}\right)=\frac{2 x+1}{x\left(x^{2}+1\right)}$.
Determine the antiderivatives $F:(0 ;+\infty) \rightarrow \mathbb{R}$ of the function $f$.
Determine the antiderivatives $F:(0 ;+\infty) \rightarrow \mathbb{R}$ of the function $f$.