### Home > APCALC > Chapter 11 > Lesson 11.2.3 > Problem11-69

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. Homework Help ✎

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

Express the numerator as $(x2 + 1) - 1$, then rewrite the fraction.

1. $\int _ { 1 } ^ { \infty } \frac { 1 } { e ^ { x } } d x$

$=\lim\limits_{b\to\infty}\int_b^\infty e^{-x}dx$

1. $\int \sec(2x) \tan(2x)dx$

$\frac{d}{du}\sec(u)=\sec(u)\tan(u)$