Q. 15

# Integrate the rat

Let

1 = A(x-1)(x2+1) + B(x+1)(x2+1) + (Cx + D)(x2 - 1)

1 = A(x3 + x – x2 -1) + B(x3 + x + x2 + 1) + Cx3 + Dx2 - Cx - D

1 = (A + B + C)x3 + (-A + B + D)x2 + (A + B - C)x + (-A + B - D)

Equating the coefficients of x3, x2, x and constant term, we get,

(A + B + C) = 0

(-A + B + C) = 0

(A + B - C) = 0

(-A + B - D) = 0

On solving these equations, we get,

A =

Therefore,

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