2. Determine whether the following integrals converge.
Improper integral 2nd type, problem at x=0.
Compare the integrand to
Since the second integral diverges (p>1), so does the original one.
Type 2 improper integral, problem spot at x=0.
Chose comparision function
(using L'Hospital rule)
Therefore, the original function behaves similarly to g(x) near 0. Since g(x)=ln(x) go slowly to as , it diverges, and so does the original integral.