Let

(taking cos³x common)

Put tan x = t

⇒ sec²x dx = dt (Differentiating both sides)

When x = 0, t = tan 0 = 0

So, the new limits are 0 and1.

Substituting this in the original integral,

Put t³ = u

⇒ 3t²dt = du (Differentiating both sides)

When t = 0, u = 0³ = 0

When t = 1, u = 1³ = 1

So, the new limits are 0 and1.

Substituting this in the original integral,

Recall