CPM Homework Help : CALC Problem 10-31

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.

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

$\int \frac { 1 } { 2 y ( 3 - y ) } d x$
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.

$\int \frac { 1 } { 1 - 2 x } d x$
Hint (d):
Use the Reverse Chain Rule or substitution.
Using substitution, let $u = 1-2x$ .