Mathematics

Evaluate :
$$ \int{ {e}^{x} \left[ \dfrac { 1 + \text{x log x}}{x} \right]} dx$$ 


SOLUTION
$$\displaystyle\int e^x\left(\dfrac{1+xlog x}{x}\right)dx$$
$$=\displaystyle\int \dfrac{e^x}{x}dx+\displaystyle\int e^xlog xdx$$
$$x=log x$$ $$\Rightarrow dx=\dfrac{1}{x}dx$$
$$dV=e^xdx$$ $$\Rightarrow V=e^x$$
$$=\displaystyle\int \dfrac{e^x}{x}dx+e^xlog x-\displaystyle\int \dfrac{e^x}{x}dx+c$$
$$=e^x log x+c$$
Where C is the constant of integration.
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Subjective Medium Published on 17th 09, 2020
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