What is the antiderivative of y=(sin2x)(cos2x)?

We'll evaluate the indefinite integral of the given
function to determine the antiderivative.

We'll re-write
the given function using the double angle identity:

y =
2sin 2x*cos 2x/2

y = sin
(4x)/2

`int` sin 2x*cos 2x dx = `int` sin (4x)
dx/2

Let 4x = t => 4dx = dt => dx =
dt/4

`int` sin (4x) dx/2 = `int` sin t
dt/8

`int` sin t dt/8 = - cos t/8 +
C

`int` sin 2x*cos 2x dx = - cos (4x)/8 +
C

The antiderivative of the given function is
the original function Y = - cos (4x)/8 + C.