Determine if the improper integral converges and, if so, evaluate it.
a) z [infinity] 2 x−3dx
b) z [infinity] 0 e−3x dx
c) z 0 −[infinity] e−3x dx
d) z 7 0 x ln x dx
e) z 0 −[infinity] xe−x2 dx
f) z 1 0 dx x(2x 5)