Integrate the rational functions.

Let

1 = A(x-1)(x^{2}+1) + B(x+1)(x^{2}+1) + (Cx + D)(x^{2} - 1)

1 = A(x^{3} + x – x^{2} -1) + B(x^{3} + x + x^{2} + 1) + Cx^{3} + Dx^{2} - Cx - D

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

Equating the coefficients of x^{3}, x^{2}, 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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