∫ 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)