Mathematics

$$\int x log x dx =?$$


SOLUTION
$$\displaystyle \int x\log x d x$$
Integrating by parts
$$\implies \log x\displaystyle\int  x d x-\int \bigg(\frac{d(\log x)}{d x}\bigg)\bigg(\int x d x\bigg)d x=\log x\bigg(\dfrac{x^2}{2}\bigg)-\int \dfrac{1}{x}\times \dfrac{x^2}{2} d x=\dfrac{x^2}{2}\log x-\dfrac{1}{2}\int x d x=\dfrac{x^2}{2}\log x-\dfrac{x^2}{4}+C $$
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Subjective Medium Published on 17th 09, 2020
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