Question

integrala de la 1 la e din ( 1+lnx-lnx)dx​

Answer 1

 

$\displaystyle\\f:(0,~+\infty)\to R, f(x)=1+\ln x\\\\\int\limits^e_1 {\Big(f(x)-\ln x\Big)} dx=\int\limits^e_1 {\Big(1+\ln x-\ln x\Big)} dx=\int\limits^e_1 {1}\,dx=x\Big|_1^e=\boxed{\bf~e-1}$

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