Find:

Let

Firstly, we rewrite the linear term as the 1^st derivative of (5 + 4x – 2x²) i.e.

On comparing the coefficients of x and the constant term, we get

-4A = 3

and 4A + B = 5

⇒ -3 + B = 5

⇒ B = 8

So,

Let I = I₁ + I₂ …(i)

For I₁,

Let 5 + 4x – 2x² = t

Taking derivatives of both the sides, we get

⇒ (4 – 4x)dx = dt

For I₂,

{Here, we add and subtract 2 to make the (a – b)²}

Now, let

Taking the derivative of both the sides, we get

So,

Now, we use the standard integral formula

Now, put back the value of t, we get

Put the value of I₁ and I₂ in eq. (i)