Solution
= Solution
On finite <intervals> the function is <continuous>, but
$$
\int_0^R\frac{x}{1+x^2}\,dx=\frac12\log(1+R^2)\longrightarrow\infty.
$$
Consequently its nonnegative <integral> on the half-line is infinite: \b[it is not <integrable>]. The divergence occurs at infinity, not at the origin.