The value of the integral $\int_{1/e}^e|ln\,x|dx$ is:
Answer & explanation
Correct answer: option 4
$\int\limits_{1/e}^1-ln\,x\,dx+\int\limits_{1}^eln\,x\,dx+x=|-x\,ln\,x+x|_{1/e}^1+|x\,ln\,x-x|_{1}^e=1-(\frac{1}{e}+\frac{1}{e})+(e-e)-(0-1)=2-\frac{2}{e}$