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Câu hỏi: Tích phân $\int\limits_{0}^{2}{\dfrac{a}{ax+3a}dx},\left( a>0 \right)$ bằng
A. $\dfrac{16a}{225}$
B. $a\log \dfrac{5}{3}.$
C. $\ln \dfrac{5}{3}.$
D. $\dfrac{2a}{15}.$
A. $\dfrac{16a}{225}$
B. $a\log \dfrac{5}{3}.$
C. $\ln \dfrac{5}{3}.$
D. $\dfrac{2a}{15}.$
Ta có $\int\limits_{0}^{2}{\dfrac{a}{ax+3a}dx}=\int\limits_{0}^{2}{\dfrac{1}{x+3}dx}=\ln \left( x+3 \right)\left| \begin{aligned}
& 2 \\
& 0 \\
\end{aligned} \right.=\ln 5-\ln 3=\ln \dfrac{5}{3}.$
& 2 \\
& 0 \\
\end{aligned} \right.=\ln 5-\ln 3=\ln \dfrac{5}{3}.$
Đáp án C.