CPM Homework Help : APCALC Problem 7-7

Integrate.

Hint:

Integrals of Exponential Functions

$\int a ^ { x } d x = \frac { 1 } { \operatorname { ln } ( a ) } \cdot a ^ { x } + C$

If $a = e$ , and because $\ln e=1$ , we have a very important special case:

$\int_{ }^{ }e^xdx=e^x+C$

Thus, the integral (or antiderivative) of $e^{x}$ differs from the original function by at most a constant.

$\int \operatorname { sin } ( 3 x ) d x$
Hint (b):
What function has a derivative of $\sin(x)$ ? How can you manipulate this function so it would have a derivative of $\sin(3x)$ ?

$\int [ ( 3 x + 1 ) ^ { 3 } + 3 x + 3 ] d x$
Hint (c):
Don't worry if you cannot figure out the antiderivative of $(3x + 1)^3$ , you could always expand it first and undo the Power Rule.