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int((x-1)dx/((2x+1)(x-2)(x-3))...

`int((x-1)dx/((2x+1)(x-2)(x-3))`

Text Solution

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Let `(x-1)/[(2x+1)(x-2)(x-3)] = A/(2x+1) + B/(x-2) + C/(x-3)`
`:. (x-1)/[(2x+1)(x-2)(x-3)] =[ A (x-2)(x-3) + B(2x+1)(x-3) + C(2x+1)(x-2]/[(2x+1)(x-2)(x-3)])`
`:. x-1 = A (x^2 - 5x + 6) + B (2x^2 - 5x -3) + C (2x^2 -3x -2)`
`:. x-1 = x^2 (A + 2B+2C) +x (-5A -5B -3C)+ (
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