### Home > APCALC > Chapter 12 > Lesson 12.3.2 > Problem12-105

12-105.

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. $\int \frac { 1 } { ( x + 1 ) ^ { 2 } + 1 } d x$

Let $u = x + 1$.
Once you rewrite the integrand, you should recognize it as a special case.

1. $\int \frac { \operatorname { cos } ( x ) } { \operatorname { sin } ^ { 2 } ( x ) + 1 } d x$

Let $u = \sin(x)$.

1. $\int \frac { \operatorname { sin } ( 2 x ) } { \operatorname { sin } ^ { 2 } ( x ) + 1 } d x$

Let $u = \sin^2(x) + 1$.

1. $\int \operatorname { ln } ( x ^ { 2 } ) d x$

$\ln(x^2) = 2\ln(x)$