Evaluate the following integral:
2x + 1 = A(x – 3)2 + B(x + 2)(x – 3) + C(x + 2)
2x + 1 = Ax2 – 3Ax + 9A + Bx2 – 5Bx – 6B + Cx + 2C
Put x = 3
7 = 5C
Put x = – 2
– 3 = 0A
– 11 = 4C
Equating coefficients of constants
– 2 = 3A + 3B + C
Thus,
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