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A

- Hướng dẫn giải

Ta có:

\(\int{f\left( x \right)\text{d}x}=\int{\frac{x+2}{x-1}\text{d}x}=\int{\frac{x-1+3}{x-1}\text{d}x}=\int{\left( 1+\frac{3}{x-1} \right)}\text{d}x=x+3.\ln \left| x-1 \right|+C=x+3.\ln \left( x-1 \right)+C\)

(Do \(x\in \left( 1;+\infty  \right)\) nên \(x-1>0\) suy ra \(\left| x-1 \right|=x-1\)).