Answer
$\ln(\dfrac{2}{5})$
Work Step by Step
Solve $\int_{-1}^{0}\dfrac{3dx}{3x-2}$
$\int_{-1}^{0}\dfrac{3dx}{3x-2}=[\ln |3x-2|]_{-1}^{0}$
This implies $[\ln |3x-2|]_{-1}^{0}=\ln |3(0)-2|-\ln |3(-1)-2|$
$=\ln |-2|-\ln |-3-2|$ (simplify)
$=\ln 2-\ln 5$
Use logarithmic properties, $\ln m-\ln n=\ln(\dfrac{m}{n})$, we have
Hence, $\int_{-1}^{0}\dfrac{3dx}{3x-2}=\ln(\dfrac{2}{5})$
