Tích phân \(I = \int\limits_1^e {\left( {\frac{1}{...

C

- Hướng dẫn giải

\(I = \int\limits_1^e {\left( {\frac{1}{x} + x} \right)\ln xdx} \\= \int\limits_1^e {\frac{1}{x}\ln xdx} + \int\limits_1^e {x\ln xdx} \\= \int\limits_0^1 {d\left( {\ln x} \right)} + \left. {\left( {\frac{{{x^2}}}{2}\ln x} \right)} \right|_1^e - \frac{1}{2}\int\limits_1^e {xdx} \\= 1 + \frac{{{e^2}}}{2} - \left. {\left( {\frac{1}{4}{x^2}} \right)} \right|_1^e = \frac{{{e^2} + 5}}{4}\)