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Câu hỏi: Khẳng định nào sau đây đúng?
A. $\int{\ln x\text{d}x=x\left( \ln x+1 \right)}$.
B. $\int{\ln x\text{d}x=x\left( \ln x+1 \right)}+C$.
C. $\int{\ln x\text{d}x=x\left( \ln x-1 \right)}+C$.
D. $\int{\ln x\text{d}x=x\left( \ln x-1 \right)}$.
A. $\int{\ln x\text{d}x=x\left( \ln x+1 \right)}$.
B. $\int{\ln x\text{d}x=x\left( \ln x+1 \right)}+C$.
C. $\int{\ln x\text{d}x=x\left( \ln x-1 \right)}+C$.
D. $\int{\ln x\text{d}x=x\left( \ln x-1 \right)}$.
Đặt $\left\{ \begin{aligned}
& u=\ln x \\
& dv=dx \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& du=\dfrac{1}{x}dx \\
& v=x \\
\end{aligned} \right.$
$\Rightarrow \int{\ln x\text{d}x=x.\ln x-\int{\text{d}x=x\ln x-x+C=x\left( \ln x-1 \right)+C}}$.
& u=\ln x \\
& dv=dx \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& du=\dfrac{1}{x}dx \\
& v=x \\
\end{aligned} \right.$
$\Rightarrow \int{\ln x\text{d}x=x.\ln x-\int{\text{d}x=x\ln x-x+C=x\left( \ln x-1 \right)+C}}$.
Đáp án C.