CPM Homework Help : APCALC Problem 7-166

Evaluate each integral below. Show your steps. If you use $u$ -substitution, be sure to change the bounds of integration.

$\int \frac { 1 } { | x | \sqrt { x ^ { 2 } - 1 } } d x$
Answer (d):
$\sec^{−1}(x) + C$ (this is a special case)

$\int _ { 1 } ^ { e } \frac { 1 } { x } \operatorname { cos } ( \operatorname { ln } ( x ) ) d x$
Hint (e):
$\frac{d}{dx}\left ( \frac{1}{x} \right )=\ln(x)$

$\int _ { - 1 } ^ { 3 } x ^ { 2 } ( x ^ { 3 } - 8 ) d x$
Hint (f):
You could use $U$ -substitution.
Or, you could expand the integrand and evaluate.