CPM Homework Help : APCALC Problem 6-54

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

$\int ( \operatorname { ln } ( 3 ) ) 3 ^ { x } d x$
Hint (a):
Remember that the derivative of $3^x = (\ln 3) · 3^x$ .

$2 \pi \int _ { 0 } ^ { 2 } x ( 2 x + 5 ) d x$
Hint (b):
Distribute the ' $x$ ' then try evaluating the integral.

$\int 4 e ^ { \operatorname { ln } ( x ) } d x$
Hint (c):
How can you rewrite $e^{\ln x}$ ?
Hint (c):
$e^{\ln x} = x$
Answer (c):
$\int ( 4 x ) d x = 2 x ^ { 2 } + C$

$\int 2 ^ { m + 2 } d m$
Hint (d):
$2^{m + 2} = 2^2 · 2^m$