### Home > CALC > Chapter 9 > Lesson 9.4.1 > Problem9-110

9-110.

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy. After evaluating each integral, write a short description of your method.

1. $\int _ { 0 } ^ { \pi } \frac { \operatorname { sin } x } { 2 - \operatorname { cos } x } d x$

Use substitution. Let $u =-\operatorname{cos}(x)$.

1. $\int _ { - 6 } ^ { 2 } | x | d x$

This integral can be evaluated by sketching the graph and using geometry.

1. $\int x ^ { 2 } e ^ { 4 x } d x$

Use integration by parts.

Let $f = x^2$ and $dg = e^{4x}$.

1. $\int _ { 0 } ^ { \infty } \frac { x } { x ^ { 2 } + 4 } d x$

Use substitution. Let $u = x^2 + 4$.