What is indefinite integral of cos^2(3x)?

To calculate the indefinite integral of the given
function, we'll have to recall the half angle
identity:

(cos 3x)^2 = (1 + cos
6x)/2

We'll evaluate the indefinite
integral:

Int (cos 3x)^2dx = Int (1 + cos
6x)dx/2

We'll apply the property of integral to be
additive:

Int (1 + cos 6x)dx/2 = Int dx/2 + Int cos 6x
dx/2

Int (1 + cos 6x)dx/2 = x/2 + sin 6x/12 +
C

The indefinite integral of the given
function is: F(x)=x/2 + sin 6x/12 + C.