$|ln\, x|\, dx$ equals $(0 < x < 1)$
Answer & explanation
Correct answer: option 1
$\int |\ln x| \, dx,\quad 0
$\ln x < 0 \Rightarrow |\ln x| = -\ln x$
$= \int -\ln x \, dx$
$= -\left(x \ln x - x\right)$
$= x - x\ln x$
The value is $x - x\ln x + C$.
$|ln\, x|\, dx$ equals $(0 < x < 1)$
Correct answer: option 1
$\int |\ln x| \, dx,\quad 0
$\ln x < 0 \Rightarrow |\ln x| = -\ln x$
$= \int -\ln x \, dx$
$= -\left(x \ln x - x\right)$
$= x - x\ln x$
The value is $x - x\ln x + C$.