Integrate the rational functions.


Let

2 = A(1 – x2) + (Bx + C)(1 – x)


2 = A + Ax2 + Bx – Bx2 + C – Cx


On comparing the coefficients of x2, x and constant term, we get,


A – B = 0


B – C = 0


A + C = 0


On solving these equations, we get,


A = 1, B =1 and C = 1


Thus,






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