CPM Homework Help : CALC Problem 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.

$\int x 5 ^ { x } d x$
Hint (a):
Use Integration by Parts.

$\int _ { 1 } ^ { e } \frac { \operatorname { ln } x + 1 } { x } d x$
Hint (b):
Use $U$ -substitution. Let $U =\operatorname{ ln}x + 1$

$\int \frac { x } { x ^ { 2 } - 4 } d x$
Hint (c):
Use integration by Partial Fractions or $U$ -substitution.

$\int \frac { x } { x ^ { 2 } + 4 } d x$
Hint (d):
Use $U$ -substitution.