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22

Integrate the function:

Given:

Let

Using partial differentiation:

let

⇒ x^{2} + x + 1 = Ax^{2} + 3Ax + 2A + Bx +2B + Cx^{2} + 2Cx + C

⇒ x^{2} + x + 1 = (2A+2B+C) + (3A+B+2C)x + (A+C)x^{2}

Equating the coefficients of x, x^{2} and constant value. We get:

(a) A + C = 1

(b) 3A + B + 2C = 1

( c) 2A+2B+C =1

After solving we get:

A=-2, B=1 and C=3

22

24

Integrate:

34

Prove:

35

Prove:

36

Prove:

37

Prove:

38

Prove:

39

Prove: