​ Cho hàm số f(x)=1/x2−3x+2 . Khi đó ​

Question

Cho hàm số \(f\left(x\right)=\frac{1}{x^{2} -3x+2}\) . Khi đó

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

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

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

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

Answer 1

Chọn D

 Ta có\( \int f\left(x\right){\rm d}x =\int \frac{1}{x^{2} -3x+2} {\rm dx} =\int \frac{1}{\left(x-1\right)\left(x-2\right)} {\rm d}x =\int \left(\frac{1}{x-2} -\frac{1}{x-1} \right){\rm d}x \)
\(=\int \frac{1}{x-2} {\rm d}x -\int \frac{1}{x-1} {\rm d}x =\ln \left|x-2\right|-\ln \left|x-1\right|+C=\ln \left|\frac{x-2}{x-1} \right|+C.\)