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Evaluate: int(x-1)/((x+1)(x-2))\ dx...

Evaluate: `int(x-1)/((x+1)(x-2))\ dx`

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`int frac{x-1}{(x+1)(x-2)}=int frac{A}{x+1}+int frac{B}{x-2}`

`=frac{A(x-2)+B(x+1)}{(x+1)(x-2)} `

` x-1=A(x-2)+B(x+1) x=2: 1=3 B: B=1 / 3 `

`frac{2}{3} int frac{d x}{x+1}+frac{1}{3} int frac{d x}{x-2} x=-1:+2=+3 A: A=2 / 3`

`frac{2}{3} log (x+1)+frac{1}{3} log (x-2)+C`

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