What is the antiderivative of sin^2 3x ?

To determine the antiderivative of the given function,
we'll have to integrate the function.

`int` (sin 3x)^2
dx

We'll use the half angle
identity:

(sin a)^2 = (1-cos
2a)/2

We'll re-write the
inetgral:

`int` (sin 3x)^2 dx = `int` (1 - cos 6x)
dx/2

`int` (1 - cos 6x) dx/2 = `int` dx/2 - (1/2)*`int` cos
6x dx

`int` (1 - cos 6x) dx/2 = x/2 - sin 6x/12 +
C

The antiderivative of the given function is
the primitive function F(x)= x/2 - sin 6x/12 + C.