Tích phân $\Large \int_1^{2} \dfrac{1}{3x-2}dx$ bằng A. $\Large \dfrac

Tích phân $\Large \int_1^{2} \dfrac{1}{3x-2}dx$ bằng

• A. A. $\Large \dfrac{2}{3}\log 2$
• B. B. $\Large \dfrac{4}{3}$
• C. C. $\Large \dfrac{2}{3}\ln 2$
• D. D. $\Large \dfrac{1}{3}\ln\dfrac{2}{3}$

Ta có $\Large \int_1^{2}\dfrac{1}{3x-2}dx = \dfrac{1}{3}\int_1^{2}\dfrac{1}{3x-2}d(3x-2)$

$\Large  = \dfrac{1}{3}\ln |3x-2|\left|_1^{2}\right. = \dfrac{1}{3}(\ln 4 - \ln 1) = \dfrac{2}{3}\ln 2$