Hoành độ giao điểm là nghiệm phương trình $|lnx| =1\\ \Leftrightarrow x=\dfrac{1}{e};x=e\\ S=\Big|\int\limits^e_{\tfrac{1}{e}} (|lnx| -1)\, dx\Big|\\ =\Big|\Big|\int\limits^e_{\tfrac{1}{e}} lnx \, dx\Big| -1\int\limits^e_{\tfrac{1}{e}} \, dx\Big|\\ =||I|-e+\dfrac{1}{e}|\\ I=\int\limits^e_{\tfrac{1}{e}} lnx \, dx \\ u=lnx \Rightarrow du=dfrac{dx}{x}\\ dv=dx \Rightarrow v=x\\ I=\int\limits^e_{\tfrac{1}{e}} lnx \, dx\\ =xlnx \Big|^e_{\tfrac{1}{e}}-\int\limits^e_{\tfrac{1}{e}} dx \\ =xlnx \Big|^e_{\tfrac{1}{e}}-x\Big|^e_{\tfrac{1}{e}}\\ =e+\dfrac{1}{e}-e+\dfrac{1}{e}\\ =\dfrac{2}{e}\\ \Rightarrow S=\Big|-e+\dfrac{3}{e}\Big|=e-\dfrac{3}{e}$
