Evaluate: <

Let I =

This can be solved by applying method of substitution:

Let, x = sin θ

∴ θ = sin^-1 x …(1)

As, x = sin θ

⇒ dx = cos θ dθ

∴ I = {∵ 1 – sin²θ = cos² θ }

⇒ I =

∴ I = sin^-1 x + C {using equation 1}