CPM Homework Help : CALC3RD Problem 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.

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

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

$\int \frac { x } { x ^ { 2 } - 4 } d x$
Hint (c):
Use partial fraction decomposition or $u$ -substitution.

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