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Ta có:
$\int\limits_1^ex\ln^3x(\ln x+2)dx$
$=\int\limits_1^ex\ln^4xdx+2\int\limits_1^ex\ln^3xdx$
$=\int\limits_1^e\ln^4xd(\frac{x^2}{2})+\int\limits_1^e\frac{x^2}{2}d(\ln^4x)$
$=\frac{x^2}{2}\ln^4x\left|\begin{array}{l}e\\1\end{array}\right.=\frac{e^2}{2}$
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