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10

Integrate the rational functions.

Let

⇒2x – 3 = A(x - 1)(2x + 3) + B(x + 1)(2x + 3) + C(x+1)( x – 1)

⇒ 2x – 3 = A(2x^{2} + x – 3) + B(2x^{2} + 5x + 3) + C(x^{2} - 1)

⇒2x - 3 = (2A + 2B + C)x^{2} + (A + 5B)x + (-3A + 3B – C)

Equating the coefficients of x^{2} and x, we get,

B =, A = and C =

Thus,

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