- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
Show that
$$\int _ { 1 } ^ { \mathrm { e } ^ { 2 } } x ^ { 3 } \ln x \mathrm {~d} x = a \mathrm { e } ^ { 8 } + b$$
where \(a\) and \(b\) are rational constants to be found.