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Q 6  Integrate the functions x^ 2 \log x

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Given function is
f(x)=x^2.\log x
We will use integration by parts method
\int x^2.\log xdx= \log x.\int x^2dx - \int(\frac{d(\log x)}{dx}.\int x^2 dx)dx\\ \\ \int x^2\log xdx = \log x.\frac{x^3}{3}- \int (\frac{1}{x}.\frac{x^3}{3})dx\\ \int x^2\log xdx = \log x.\frac{x^3}{3}- \int \frac{x^2}{3}dx\\ \int x^2\log xdx = \log x.\frac{x^3}{3}- \frac{x^3}{9}+ C

Therefore, the answer is \log x.\frac{x^3}{3}- \frac{x^3}{9}+ C
 

Posted by

Gautam harsolia

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