### Home > CALC > 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. After evaluating the integral, write a short description of 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 $U =\operatorname{ ln}x + 1$

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

Use integration by Partial Fractions or $U$-substitution.

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

Use $U$-substitution.