Evaluate the following integrals:

In this equation, we can manipulate numerator

sin³x = sin²x.sinx

∴ Now the equation becomes,

⇒

sin²x = 1 - cos²x

⇒

Now ,

Let us assume cosx = t

d(cosx) = dt

- sinx dx = dt

Substitute values of t and dt in above equation

⇒

⇒

⇒

⇒

But t = cosx

⇒