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

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.

anonymous · Answer

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.