∫ sin 2x sin 4x sin 6x dx

We need to simplify the given equation to make it easier to solve

We know 2sinAsinB = cos(A – B) – cos(A + B)

∴ sin4xsin2x =

∴ The above equation becomes

⇒

⇒

We know 2sinAcosB = sin(A + B) + sin(A – B)

∴ sin6xcos2x =

_{Also 2sinx.cosx = sin2x}

∴ sin6xcos6x =

∴ The above equation simplifies to

⇒

⇒

We know

⇒

⇒

⇒ (where c is some arbitrary constant)