CPM Homework Help : CALC Problem 7-7

Integrate.

$\int e ^ { 3 x } d x$

$\int \operatorname { sin } ( 3 x ) d x$

$\int [ ( 3 x + 1 ) ^ { 3 } + 3 x + 3 ] d x$

Hint (a):

Hint (b):

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

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.