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Đặt : $u =ln^2x\Rightarrow du=\frac{2lnx}{x}$
$\begin{array}{l}
dv = xdx \Rightarrow v = \frac{{{x^2}}}{2}\\
I = \frac{{{x^2}}}{2}{\ln ^2}x\left| {_1^e} \right. - \int_1^e {x\ln xdx} = \frac{{{e^2}}}{2} - \int_1^e {x\ln xdx}
\end{array}$
Đặt : $u=lnx\Rightarrow du=\frac{dx}{2}$
$dv=xdx\Rightarrow v=\frac{x^2}{2}$
Suy
ra :$\int_1^e {x\ln xdx} = \frac{{{x^2}}}{2}\ln x\left| {_1^e -
\frac{1}{2}} \right.\int_1^e {xdx} = \frac{{{e^2}}}{2} -
\frac{1}{4}\left( {{e^2} - 1} \right)$
Suy ra : $I = \frac{1}{4}\left( {{e^2} + 1} \right)$
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