Evaluate the following Integrals:

Let

Put x = sin θ

⇒ dx = cos θ dθ (Differentiating both sides)

Also,

When x = 0, sin θ = 0 ⇒ θ = 0

So, the new limits are 0 and.

Substituting this in the original integral,

Dividing numerator and denominator with cos²θ, we have

[∵ sec²θ = 1 + tan²θ]

Put tan θ = t

⇒ sec²θ dθ = dt (Differentiating both sides)

When θ = 0, t = tan 0 = 0

So, the new limits are 0 and.

Substituting this in the original integral,

Recall