Answer
$\pi (e-2) $
Work Step by Step
The volume of a revolution can be calculated by using integration by parts as:
$V=\pi \int_{1}^{e} (\ln x)^2\\=\pi \int_1^{e} \ln ^2 x \ dx \\=\pi e -2 \pi \int_1^e \ln x \ dx \\= \pi e -2 \pi (x \ln x|_1^e -\int_1^e dx) \\=\pi e-2 \pi e +2 \pi (e-1) \\=\pi (e-2) $
