CPM Homework Help : CALC Problem 10-54

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy. After evaluating each integral, write a short description of your method.

$\int \frac { 1 } { ( x - 1 ) ( x + 5 ) } d x$
Hint (a):
Use partial fraction decomposition.

$\int \frac { x ^ { 3 } + 2 x } { x - 1 } d x$
Hint (b):
Rewrite the integrand by using polynomial division.

$\int 5 x ^ { 2 } ( 5 x ^ { 3 } - 2 ) ^ { - 1 / 2 } d x$
Hint (c):
Use substitution. Let $u = 5x^3-2$ .

$- \int 2 \operatorname { sec } ^ { 2 } x d x$
Hint (d):
$\frac{d}{dx}\tan(x)=\sec^2(x)$