We can write it as

We also know that 2sinx.cosx = sin2x

We also know that

Here Sin4x = 2sin2x.cos2x

Using BY PART METHOD. Using the superiority list as ILATE (Inverse Logarithm Algebra Trigonometric Exponential). Taking the first function to the one which comes first in the list.

Here x is first function and Sin2x and sin4x as the second function.