Question

integral of integral sin^3(6x) cos^3 (6x)

Answer 1

\(\sin(2x) = 2\sin(x)\cos(x)\) -- That might come in handy.

\(\cos^{2}(x) = 1 - \sin^{2}(x)\) -- That might be another way to go.

Seriously, just try something. You won't break it.

Answer 2

I would try\[\sin^3(6x)\cos^3(6x)=\sin^3(6x)\cos^2(6x)\cos(6x)\]\[=\sin^3(6x)[1-\sin^2(6x)]\cos(6x)=[\sin^3(6x)-\sin^5(6x)]\cos(6x)\]