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.
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.
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