Evaluate the given definite integral.

Name: Evaluate the given definite integral.
Brand: Quizplus
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Question

Quizplus · Accepted Answer

The integral is evaluated using integration by parts with $u=\ln x$ and $dv=e^{2\ln x}dx=x^2dx$. This gives
$$\int_1^e x^2\ln x \, dx = \left[\frac{x^3\ln x}{3}ight]_1^e -\int_1^e \frac{2x^2}{3} dx = \frac{e^3}{3}(1+\ln e) - \frac{2e^3-2}{9} - \frac{1}{3} = \frac{1}{9}(7e^3-9).$$
Therefore, the correct answer is $\boxed{	extbf{(D)}\ 11eb12b0_a973_93fb_b394_bd90d5c643f3_TB7866_11}$.

Evaluate the Given Definite Integral