Question

Intergral and converges

Answer 1

For which value of p converges these integral
\[\int\limits_{0}^{1/2}\frac{ dx }{ x \left| \ln(x) \right|^p }\]
and
\[\int\limits_{2}^{∞}\frac{ dx }{ x \left| \ln(x) \right|^p }\]

My conclusion is for p≥1 both integral converges. Is that correct?

Answer 2

Good question.