xlogx integrate the function
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Sia ? 6 years, 5 months ago
Let logx = 1st function and x be the second function.
Therefore,
{tex}\left.\log x \int x \cdot d x-\int\left(\frac{d(\log x)}{d x}\right) \cdot \int x \cdot d x\right) \cdot d x{/tex}
{tex}=\log x \frac{x^{2}}{2}-\int\left(\frac{1}{x} \cdot \frac{x^{2}}{2}\right) \cdot d x{/tex}
{tex}=\log x \cdot \frac{x^{2}}{2}-\int\left(\frac{x}{2}\right) \cdot d x{/tex}
{tex}=\log x \cdot \frac{x^{2}}{2}-\frac{1}{2} \cdot \frac{x^{2}}{2}{/tex}
{tex}=\log x \cdot \frac{x^{2}}{2}-\frac{x^{2}}{4}{/tex}
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