Evaluate ∫ x^2log x dx.

Question 83

MediumOriginal question

Evaluate $\int x^{2}\log x\,dx$ .

\frac{x^{3}\log x}{3} + \frac{x^{3}}{9} + C

Correct answerYour answer

\frac{x^{3}\log x}{3} - \frac{x^{3}}{3} + C

Correct answerYour answer

\frac{x^{3}\log x}{3} - \frac{x^{3}}{9} + C

Correct answerYour answer

2x\log x + x + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Take $u = \log x$ and $dv = x^{2}\,dx$ : $du = \frac{dx}{x}$ , $v = \frac{x^{3}}{3}$ .
$\frac{x^{3}\log x}{3} - \int \frac{x^{2}}{3}\,dx = \frac{x^{3}\log x}{3} - \frac{x^{3}}{9} + C$ .

Worth noting

$-\frac{x^{3}}{3}$ forgets to integrate $\frac{x^{2}}{3}$ , which gives $\frac{x^{3}}{9}$ .

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