We are integrating f(x) = 9cos(9x) + 3x²: 
a) Apply the sum rule

b) Calculate each antiderivative
<u>First integral</u>

1. Take out the constant

2. Apply u-substitution, where u is 9x

3. Take out the constant (again)

4. Take the common integral of cos, which is sin

5. Substitute the original function back in for u and simplify
6. Always remember to add an arbitrary constant, C, at the end

<u>Second integral</u>

1. Take out the constant

2. Apply the power rule,
, where <em>a</em> is your exponent
⇒ 
3. Add the arbitrary constant

c) Add the integrals
sin(9x) + C + x³ + C = sin(9x) + x³ + C
Notice the two arbitrary constants. Since we do not know what either constant is, we can combine them into one arbitrary constant.
<h3>
Answer:</h3>
F(x) = sin(9x) + x³ + C