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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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