Nếu $\Large \int f(x)dx=\dfrac{1}{x}+\ln x+C$ thì $\Large f(x)$ là $\L

Nếu $\Large \int f(x)dx=\dfrac{1}{x}+\ln x+C$ thì $\Large f(x)$ là

• A. $\Large f(x)=\sqrt{x}+\ln x+C$.
• B. $\Large f(x)=-\sqrt{x}+\dfrac{1}{x}+\ln x+C$.
• C. $\Large f(x)=\dfrac{x-1}{x^2}$.
• D. $\Large f(x)=-\dfrac{1}{x^2}+\ln x+C$.

Chọn C

$\Large \int f(x)dx=\dfrac{1}{x}+\ln x+C$ $\Large \Rightarrow f(x)={\left(\dfrac{1}{x}+\ln x+C\right)}'=-\dfrac{1}{x^2}+\dfrac{1}{x}=\dfrac{x-1}{x^2}$.