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Câu hỏi: Xét $\int\limits_{1}^{e}{\dfrac{2\ln x+1}{x}}dx$, nếu đặt $t=\ln x$ thì $\int\limits_{1}^{e}{\dfrac{2\ln x+1}{x}}dx$ bằng
A. $\int_{0}^{2}{(2t+1)}dt$.
B. $\int\limits_{0}^{1}{\left( 2t+1 \right)}dt$.
C. $\int\limits_{1}^{e}{\left( 2t+1 \right)}dt$.
D. $\int\limits_{0}^{e}{\left( 2t+1 \right)}dt$.
A. $\int_{0}^{2}{(2t+1)}dt$.
B. $\int\limits_{0}^{1}{\left( 2t+1 \right)}dt$.
C. $\int\limits_{1}^{e}{\left( 2t+1 \right)}dt$.
D. $\int\limits_{0}^{e}{\left( 2t+1 \right)}dt$.
Đặt $t=\ln x$ suy ra $dt=\dfrac{1}{x}dx$.
Khi $x=1\Rightarrow t=0$
Khi $x=e\Rightarrow t=1$
Khi đó $\int\limits_{1}^{e}{\dfrac{2\ln x+1}{x}}dx=\int\limits_{0}^{1}{\left( 2t+1 \right)}dt$.
Khi $x=1\Rightarrow t=0$
Khi $x=e\Rightarrow t=1$
Khi đó $\int\limits_{1}^{e}{\dfrac{2\ln x+1}{x}}dx=\int\limits_{0}^{1}{\left( 2t+1 \right)}dt$.
Đáp án B.