CPM Homework Help : APCALC Problem 10-45

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method.

$\int \frac { \operatorname { ln } ( x + 5 ) } { 2 x + 10 } d x$
Hint (a):
Use substitution. Let $u = \ln(x + 5)$ .
More Help:
$2x + 10 = 2(x + 5)$

$\int_{ }^{ }\frac{1}{2y(3-y)}dy$
Hint (b):
Use partial fraction decomposition to rewrite the integrand.

$\int e ^ { \operatorname { ln } ( x ) } d x$
Hint (c):
$e^{\ln(x)}$ can be simplified.

d. $\int \frac { 1 } { 1 - 2 x } d x$

Hint (d):

Use the Reverse Chain Rule or substitution.
Using substitution, let $u = 1 - 2x$ .