Use integration by parts to find \(\int \frac { \ln ( 3 x ) } { x ^ { 2 } } \mathrm {~d} x\).
The region bounded by the curve \(y = \frac { \ln ( 3 x ) } { x }\), the \(x\)-axis from \(\frac { 1 } { 3 }\) to 1 , and the line \(x = 1\) is rotated through \(2 \pi\) radians about the \(x\)-axis to form a solid.
Find the exact value of the volume of the solid generated. [0pt]
[7 marks]