2. Determine whether the following integrals converge.

2.1

Improper integral 2nd type, problem at x=0.

Compare the integrand to

Since the second integral diverges (p>1), so does the original one.

2.2

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.