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Câu hỏi: Tìm họ nguyên hàm $F\left( x \right)$ của hàm số $f\left( x \right)=\dfrac{x-1}{{{x}^{2}}},x\ne 0$.
A. $F\left( x \right)=\ln x+\dfrac{1}{x}+C$.
B. $F\left( x \right)=\ln \left| x \right|-\dfrac{1}{x}+C$.
C. $F\left( x \right)=-\ln \left| x \right|+\dfrac{1}{x}+C$.
D. $F\left( x \right)=\ln \left| x \right|+\dfrac{1}{x}+C$.
A. $F\left( x \right)=\ln x+\dfrac{1}{x}+C$.
B. $F\left( x \right)=\ln \left| x \right|-\dfrac{1}{x}+C$.
C. $F\left( x \right)=-\ln \left| x \right|+\dfrac{1}{x}+C$.
D. $F\left( x \right)=\ln \left| x \right|+\dfrac{1}{x}+C$.
Xét $F\left( x \right)=\int{\dfrac{x-1}{{{x}^{2}}}}dx$ $=\int{\left( \dfrac{1}{x}-\dfrac{1}{{{x}^{2}}} \right)dx}=\int{\dfrac{1}{x}}dx-\int{\dfrac{1}{{{x}^{2}}}}dx=\ln \left| x \right|+\dfrac{1}{x}+C$.
Đáp án D.