CPM Homework Help : APCALC Problem 6-35

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

$\int ( 6 ^ { x } - 3 \operatorname { sec } ( x ) \operatorname { tan } ( x ) ) d x$
Hint (a):
What two functions have derivative of $6^{x}$ and $3\sec\left(x\right)\tan\left(x\right),$ respectively?
Answer (a):
$\frac{6^{x}}{\text{ln} 6}-3\text{sec}x+C$

$\pi \int _ { 0 } ^ { 2 } ( ( 2 x ) ^ { 2 } - ( x ^ { 2 } ) ^ { 2 } ) d x$
Hint (b):
$\left(2x\right)^{2} − \left(x^{2}\right)^{2} = 4x^{2} − x$

$\int _ { 1 } ^ { 4 } \frac { 3 x ^ { 2 } + 13 x - 10 } { x + 5 } d x$
Hint (c):
Factor.

$\int 6 m ^ { - 4 / 3 } d m$
Hint (d):
Undo the Power Rule.