Use integration to find the exact value of [integral of] (9-cos^2(4x)) dx
- you cannot integrate cos^2(4x) without making substitutions first. Use the cos^2(x) + sin^2(x) = 1 identity with the cos(2x)=cos^2(x)-sin^2(x), rearrange to get the identity cos(2x) = 2cos^2(x) - 1, then cos^2(x) = 0.5(cos(2x)+1)
2) use this new identity to rewrite 6cos^2(4x), which will become 3cos(8x)+3
3) integrate the constant 9 to become 9x
4) integrate -(3cos(8x)+3) to get -(3/8sin(8x) - 3x)
5) final answer is 6x - 3/8(sin(8x))
