Consider the improper integral

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

\displaystyle \int_{1}^{\infty}\frac{\ln x}{x^{2}}\,dx

. Identify which factor should be differentiated first so that each successive integral involves a term whose absolute value decreases like

\tfrac{1}{x^{p}}

with

p>1

, and briefly explain how this choice guarantees convergence.