What is the integral of `int sin^2(3x)*cos^2(3x) dx`

`int sin^2 (3x)
cos^2 (3x) dx`

`` We know that:

`sin(3x)= 3sinx -4sin^3 x
`

`cos(3x)= 4cos^3 x -3cosx `

`==gt int (3sinx-4sin^3 x
)(4cos^3 x -3cosx) dx `

`==gt int (12sinxcos^3 x-9sinxcosx -16sin^3 x cos^3 x
+12cosx sin^3 x) dx `

`==gt 12int sinxcos^3 x dx -9int sinxcosx dx`

`-16int sin^3 x cos^2 x dx+ 12int cosx sin^3 x dx`

`==gt 12int sinx
cos^3 x dx `

`==gt u= cosx ==gt du= sinx dx `

`==gt 12int
sinx u^3 du/sinx = 12int...