Integrate the functions.

Let x + 2 =

⇒ x + 2 = A(4 -2x) + B

Now, equating the coefficients of x and constant term on both sides, we get,

-2A = 1

⇒ A =

4A + B = 2

⇒ B = 4

⇒ x + 2 =

Now,

⇒

Now, let us consider,

Let 4x – x² = t

⇒ (4 -2x) dx= dt

…(1)

And, Now let us consider,

Then, 4x – x² = -(-4x + x²)

= (-4x + x² + 4 – 4)

= 4 – (x - 2)²

= (2)² – (x - 2)²

…(2)

using eq. (1) and (2), we get,

⇒