CPM Homework Help : APCALC Problem 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.

$\int \frac { 1 } { ( x + 1 ) ^ { 2 } + 1 } d x$
Hint (a):
Let $u = x + 1$ .
Once you rewrite the integrand, you should recognize it as a special case.

$\int \frac { \operatorname { cos } ( x ) } { \operatorname { sin } ^ { 2 } ( x ) + 1 } d x$
Hint (b):
Let $u = \sin(x)$ .

$\int \frac { \operatorname { sin } ( 2 x ) } { \operatorname { sin } ^ { 2 } ( x ) + 1 } d x$
Hint (c):
More Help (c):
Let $u = \sin^2(x) + 1$ .

$\int \operatorname { ln } ( x ^ { 2 } ) d x$
Hint (d):
$\ln(x^2) = 2\ln(x)$