Originally Posted by

**Moo** **Text**

Let $\displaystyle C_0(\mathbb{R}^+)$ be the set of functions defined over $\displaystyle \mathbb{R}^+$, continuous, with real values.

$\displaystyle f \in C_0(\mathbb{R}^+)$. Let F be the antiderivative of f that annulates in 0.

Let E be the subset of functions f in $\displaystyle C_0(\mathbb{R}^+)$ such that $\displaystyle I(f)=\int_0^\infty \frac{F(t)}{(1+t)^2} \ dt$ converges.

**Problem :**

Find an example for f (necessarily not of constant sign) in E and such that $\displaystyle \int_0^\infty \frac{f(t)}{1+t} \ dt$ diverges.