CPM Homework Help : APCALC Problem 11-69

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.

$\int \frac { x ^ { 2 } } { x ^ { 2 } + 1 } d x$
Hint (a):
Express the numerator as $(x^2+1)-1$ , then rewrite the fraction.

$\int _ { 1 } ^ { \infty } \frac { 1 } { e ^ { x } } d x$
Step (b):
$=\lim\limits_{b\to\infty}\int_b^\infty e^{-x}dx$

$\int \sec(2x) \tan(2x)dx$
Hint (c):
$\frac{d}{du}\sec(u)=\sec(u)\tan(u)$