Question

integral of (ln(3x-1))/(3x-1)

Answer 1

$\int \frac{ln(3x-1)}{3x-1}dx = \frac{1}{3}\int\frac{ln(3x-1)}{3x-1}d(3x-1) = \frac{1}{3}\int ln(3x-1)d(ln(3x-1)) = \frac{1}{3} * \frac{ln^2(3x-1)}{2} + c= \frac{1}{6}ln^2(3x-1) + c\\ Answer: \frac{1}{6}ln^2(3x-1) + c$

Answer 2

Ответ:

$\dfrac{1}{6}ln^2(3x-1)+C$

Пошаговое объяснение:

$\int {\dfrac{ln(3x-1)}{3x-1} } \, dx =\dfrac{1}{3} \int {ln(3x-1) \, d(ln(3x-1))=\dfrac{1}{6}ln^2(3x-1)+C$