In this equation, we can manipulate numerator

Cos³x = cos²x.cosx

∴ Now the equation becomes,

⇒

Cos²x = 1 - sin²x

⇒

Now,

Let us assume sinx = t

d(sinx) = dt

cosx dx = dt

Substitute values of t and dt in the above equation

⇒

⇒

⇒

⇒

But t = sinx

⇒ .