Chapter 8.6, Problem 63E

(a)

To determine

To calculate: The pattern for values of ${\displaystyle \int x^n\ln xdx}$ for $n=1,2,3$.

(b)

To determine

A general rule for evaluating the integral ${\displaystyle {\int }_{}^{}{x}^n\ln xdx}$ for integer $n\ge 1$.