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.