∫[2,3]u^2/(u^2-1)du
=∫[2,3][1+1/(u^2-1)]du
=∫[2,3][1+1/2*1/(u-1)-1/2*1/(u+1)]du
=[u+1/2ln(u+1)+1/2ln(u-1)][2,3]
=1+1/2ln4-1/2ln3+1/2ln2
=1+3/2*ln2-1/2ln3