For all questions, please show all relevant work.

1. (5 points) Compute the partial fraction decomposition of

the rational function

32

x(x

2 + 4)2

.

Note: Do not find this function’s integral.

2. (5 points) Determine whether following integral converges

or diverges

Z ∞

3

dx

ln(x)

.

Hint: ln(x) ≤ x when x > 0.