We know that Sin3x = 3Sinx - 4Sin³x

Sin³x = (3Sinx - Sin3x)/4

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 sinx and sin3x as the second function.