Determine which values of $p$ the following integrals converge. Give your answer in each case by selecting the appropriate inequality and then entering a numerical value in the box to define a range of $p$ values for which the integral converges. If the integral never converges, select = and enter none for the numerical value. In either case be sure that you can rigorously prove convergence and divergence for different values of $p$.

(a) $\int_2^\infty\,{dx\over x(\ln(x))^p}$ : $p$ ? > >= < <= =

(b) $\int_2^\infty\,{\ln(x) dx\over x^p}$ : $p$ ? > >= < <= =