### Home > APCALC > Chapter 10 > Lesson 10.1.4 > Problem10-45

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.

1. $\int \frac { \operatorname { ln } ( x + 5 ) } { 2 x + 10 } d x$

Use substitution. Let $u = \ln(x + 5)$.

$2x + 10 = 2(x + 5)$

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

Use partial fraction decomposition to rewrite the integrand.

1. $\int e ^ { \operatorname { ln } ( x ) } d x$

$e^{\ln(x)}$ can be simplified.

d. $\int \frac { 1 } { 1 - 2 x } d x$

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