CPM Homework Help : APCALC 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. Homework Help ✎

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