Integrate the function:

Given:

Let

Using partial differentiation:

let

⇒ 1 = A – Ax² + Bx – Bx² + Cx + Cx²

⇒ 1 = A + (B+C)x + (-A-B+C)x²

Equating the coefficients of x, x² and constant value. We get:

(a) A = 1

(b) B+C = 0 ⇒ B = -C

(c) -A –B +C =0

⇒ -1 – (-C) +C = 0

⇒ 2C = 1 ⇒ C = 1/2

So, B = -1/2

Put these values in equation (1)