Question

Consider the improper integral from 2 to infinite [x^2 dx] / [(x-1)^2 * (x+3)]
a) Decide directly from the definition whether this integral converges
or diverges.
b) Use the limit comparison theorem to decide whether this integral
converges or diverges.

Answer 1

a) The integral does not converge by computation.
b) you can use limit comparison of the integrand to something like 1/x to show the same thing.