009B Sample Final 2, Problem 7

Evaluate the following integrals or show that they are divergent:

a) $\int _{1}^{\infty }{\frac {\ln x}{x^{4}}}~dx$

b) $\int _{0}^{1}{\frac {3\ln x}{\sqrt {x}}}~dx$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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