Mathematics

Solve :
$$ \int x^x ln (ex) dx $$


SOLUTION
$$\begin{array}{l} \int { { x^{ x } }\left( { \ln { \left( { ex } \right)  }  } \right)  } dx \\ \int { { x^{ x } }\left( { 1+\ln { x }  } \right)  } dx \\ Let\, { x^{ x } }=t \\ \log  t=x\log  x \\ \frac { 1 }{ t } =1+\log  x \\ \frac { { dt } }{ { dx } } ={ x^{ x } }\left( { 1+\log  x } \right)  \\ \int { dt } =t+c={ x^{ x } }+C \end{array}$$
Hence,
Solved.
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Subjective Medium Published on 17th 09, 2020
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