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34

Prove:

Given:

Using partial differentiation:

⇒ 1 = Ax^{2} +Ax+ B+Bx+ Cx^{2}

⇒ 1 = B + (A+B)x + (A+C)x^{2}

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

(a) B = 1

(b) A + B = 0 ⇒ A = -B ⇒ A = -1

( c) A + C =0 ⇒ C = -A ⇒ C = 1

Put these values in equation (1)

⇒ L.H.S = R.H.S

Hence proved.

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24

Integrate:

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Prove:

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Prove:

36

Prove:

37

Prove:

38

Prove:

39

Prove: