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

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`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...

(The entire section contains 238 words.)

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