### Home > APCALC > Chapter 8 > Lesson 8.4.1 > Problem8-143

8-143.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each part. Evaluate each integral and briefly describe your method.

1. $\int x 5 ^ { x } d x$

Use integration by parts.

1. $\int _ { 1 } ^ { e } \frac { \operatorname { ln } ( x ) + 1 } { x } d x$

Use $u$-substitution. Let $u =\ln(x) + 1$.

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

Use partial fraction decomposition or $u$-substitution.

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

Use $u$-substitution.