∫ sin x cos 2x sin 3x dx

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

∴ sin3xcos2x =

∴ The given equation becomes

⇒

⇒

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

∴ sin5xsinx =

Also sin²x =

∴ Above equation can be written as

⇒

⇒

We know

⇒

⇒

⇒

NOTE: – Whenever you are solving integral questions having trigonometric functions in the product then the first thing that should be done is convert them in the form of addition or subtraction.