Mathematics

# Evaluate:$\displaystyle\int{\ln{\left(\dfrac{1}{{e}^{x}}\right)}dx}$

##### SOLUTION
$\displaystyle\int{\ln{\left(\dfrac{1}{{e}^{x}}\right)}dx}$
$=\displaystyle\int{\ln{\left({e}^{-x}\right)}dx}$
$=\displaystyle\int{-x\ln{e}dx}$
$=-\displaystyle\int{x\,dx}$
$=\dfrac{-{x}^{2}}{2}+c$ 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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