### Home > APCALC > Chapter 6 > Lesson 6.1.4 > Problem6-54

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.

1. $\int ( \operatorname { ln } ( 3 ) ) 3 ^ { x } d x$

Remember that the derivative of $3^x = (\ln 3) · 3^x$.

1. $2 \pi \int _ { 0 } ^ { 2 } x ( 2 x + 5 ) d x$

Distribute the '$x$' then try evaluating the integral.

1. $\int 4 e ^ { \operatorname { ln } ( x ) } d x$

How can you rewrite $e^{\ln x}$?

$e^{\ln x} = x$

$\int ( 4 x ) d x = 2 x ^ { 2 } + C$

1. $\int 2 ^ { m + 2 } d m$

$2^{m + 2} = 2^2 · 2^m$