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Q 5  Integrate the functions x \log 2x

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Given function is
f(x)=x.\log 2 x
We will use integration by parts method
\int x.\log 2xdx= \log 2x.\int xdx - \int(\frac{d(\log 2x)}{dx}.\int x dx)dx\\ \\ \int x\log 2xdx = \log 2x.\frac{x^2}{2}- \int (\frac{2}{2x}.\frac{x^2}{2})dx\\ \int x\log 2xdx = \log 2x.\frac{x^2}{2}- \int \frac{x}{2}dx\\ \int x\log 2xdx = \log 2x.\frac{x^2}{2}- \frac{x^2}{4}+ C

Therefore, the answer is \log 2x.\frac{x^2}{2}- \frac{x^2}{4}+ C

Posted by

Gautam harsolia

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