Evaluate ∫xlog⁡xdx

Correct option is 3x22log⁡x−14x2+C

Questions

$Evaluate \int x \log x d x$

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x24log⁡x−14x2+C

x22log⁡x−12x2+C

x22log⁡x−14x2+C

None of these

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detailed solution

Correct option is C

∫II xlog⁡xdx=log⁡x∫xdx−∫ddx(log⁡x)∫xdxdx=(log⁡x)x22−∫1xx22dx=x22log⁡x−12∫xdx=x22log⁡x−12x22+C=x22log⁡x−14x2+C

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