Integral 4 sin2x cos4x cos6x)dx

[tex]
\int{4\sin{(2x)}\cos{(4x)}\cos{(6x)}}dx\\
=\int{2\cdot(\sin{(2x+4x)}+\sin{(2x-4x)})\cdot\cos{(6x)}}dx\\
=\int{(2\sin{(6x)}\cos{(6x)}+2\sin{(-2x)}\cos{(6x)})}dx\\
=\int{(\sin{(6x+6x)}+\sin{(6x-6x)})}dx+\int{(\sin{(-2x+6x)}+\sin{(-2x-6x)})}dx\\
=\int{\sin{(12x)}}dx+\int{(\sin{(4x)}-\sin{(8x)})}dx\\
=-\frac{1}{12}\cos{(12x)}-\frac{1}{4}\cos{(4x)}+\frac{1}{8}\cos{(8x)}+C
[/tex]